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The Zürich Experience: One Decade of Three-Dimensional High-Resolution Computed Tomography

2002; Lippincott Williams & Wilkins; Volume: 13; Issue: 5 Linguagem: Inglês

10.1097/00002142-200210000-00003

1536-1004

Ralph Müller,

Radiomics and Machine Learning in Medical Imaging

INTRODUCTION Bone mineral measurements frequently are used to diagnose metabolic bone diseases such as osteoporosis. Before age 50 years, such diseases affect only a few people, whereas in old age, few individuals are left without fractures due to age-or disease-related reduction of bone strength. Although many older persons may lose bone, as expressed by a decrease in bone density, not all develop fractures. This is not unexpected, as bone density is not the sole determinant of fracture risk. Neuromuscular function and environmental hazards influencing the risk of fall, force of impact, and bone strength are equally important factors (1). Bone mineral density (BMD), geometry of bone, microarchitecture of bone, and quality of the bone material all are components that determine bone strength as defined by the bone's ability to withstand loading. On average, 70–80% of the variability in bone strength in vitro is determined by its density (2). On an individual basis, density alone accounts for 10–90% of the variation in the strength of trabecular bone (3). This also means that 90–10% of the variation in strength cannot be explained by bone density. Preliminary data have shown that predicting trabecular bone strength can be greatly improved by including architectural parameters in the analysis (4–6). Quantitative bone morphometry is a method to assess structural properties of the trabecular bone. Trabecular morphometry traditionally has been assessed in two dimensions, where the structural parameters are either inspected visually or measured from sections, and the third dimension is added on the basis of stereology (7,8). The conventional approach to morphologic measurements typically entails substantial preparation of the specimen, including embedding in methylmethacrylate, followed by sectioning into slices. Although the method offers high spatial resolution and high image contrast (Fig. 1A and B), it is a tedious and time-consuming technique. Particularly limiting is the destructive nature of the procedure, which prevents the specimen from being used for other measurements such as analysis in different planes. The latter is highly desirable because of the anisotropic nature of trabecular bone (9–11). To overcome some of the limitations of the analysis of two-dimensional (2D) histologic sections, several three-dimensional (3D) measurement and analysis techniques are being investigated. Traditionally, the most common technique is the use of stereo-or scanning microscopy to assess 3D structural indices qualitatively. In using these methods researchers were able to demonstrate the loss of 3D connectivity in the trabecular network with age and the involved modeling processes and sites by visual observation (12). Structural age dependency also could be demonstrated by using a surface-stained block grinding technique that allowed a semiquantitative combined 2d and 3D histomorphometric analysis of the spine with the help of stereomicroscopy (13). In the past, the method of serial sectioning has been used to explore the third dimension quantitatively (14). This technique provides 3D images of trabecular bone with high resolution and high quality where the 3D structure is reconstructed based on microscopic optical images from individual contiguous sections. However, the method also entails substantial preparation of the specimen, including embedding in black resin, followed by sectioning into thin slices as well as surface treatment of contrast enhancement. With such methods, quantitative measurement of 3D connectivity and other structural properties such as volume fraction and surface area are possible on a truly 3D basis. Nevertheless, by using such preparation the bone samples are no longer available for other static and dynamic histomorphometric analyses. Also, being truly destructive, the serial sectioning technique does not allow subsequent mechanical testing or other secondary measurements because the samples are destroyed during sample preparation. Microcomputed tomography (μCT) is an alternate approach to image and quantify trabecular bone in three dimensions. The field was pioneered by Feldkamp et al. (15), who used a microfocus x-ray tube as a source, an image intensifier as a 2D detector, and a cone-beam reconstruction algorithm to create a 3D object with a typical resolution of 50 μm. Others used synchrotron radiation to obtain spatial resolutions on the order of microns (16,17). Comparison of different μCT methods was discussed by Bonse et al. (16). Whereas the early implementations of 3D microtomography focused more on the technical and methodologic aspects of the systems and required equipment not normally available to a large public, a more recent development (18) emphasized the practical aspects of microtomographic imaging. The project was aimed at enlarging the availability of the technology in basic research as well as in clinical laboratories. That system is based on a compact fan-beam type of tomograph, also referred to as desk-top μCT. Desk-top μCT has been used extensively for different research projects involving microstructural bone and biomaterials (19). Although all of these techniques allow measurement and analysis of 3D trabecular bone on a microstructural level (10–50 μm image resolution) (Fig. 1C and D), they remain invasive and are restricted to the analysis of relatively small samples of excised bone. Moreover, the harvesting of bone biopsies is painful and, typically, the patient has to be in ambulant care or sometimes even hospitalized for a couple of days. Probably even more important is that the structural properties cannot be assessed repetitively for a specific location. This would be mandatory to follow changes in the bone architecture over time in age-related bone loss or to monitor treatment efficacy in individual subjects.FIG. 1.: Two-dimensional (A; histology) and 3D (C; microtomography) trabecular bone of a transiliac crest bone biopsy of a 37-year-old man with no known bone disorders. The distinct platelike structure as typically found in young individuals is easily seen. Two-dimensional (B; histology) and 3D (D; microtomography) trabecular bone of a 73-year-old osteoporotic woman. The bone structure is loosely formed with the original platelike bone structure almost completely resolved resulting in an almost rodlike structure with fewer and thinner trabecular elements. (Histology figures courtesy Hilde van Campenhout, KU Leuven, Belgium.)This article focuses on technical and clinical developments that took place at the Institute for Biomedical Engineering, Swiss Federal Institute of Technology (ETH) and University of Zürich, Switzerland, over the last 10 years, which were related to 3D high-resolution imaging using x-ray CT. There also have been other developments in the field worldwide and some of them will be mentioned here, but most of the data are limited to the “Zürich experience” as a single body of work. HIGH-RESOLUTION QUANTITATIVE CT Today, quantitative computed tomography (QCT) is a widely used and accepted method to measure bone density precisely. QCT of the spine (axial QCT) was described by several investigators (20,21). Peripheral QCT (pQCT) as described by Rüegsegger (22) and Müller et al. (23) was used to diagnose metabolic bone diseases such as osteoporosis and to monitor the effectiveness of treatment regimens. An ideal QCT system should have sufficient 3D spatial and temporal resolution to visualize and quantitatively study anatomic static and dynamic structural relationships to biologic functions of all macroscopic anatomic structures of interest in all regions of the body. Current CT scanners are far from this goal. Presently axial QCT and pQCT are extended to provide quantitative structural information of bones in addition to pure densitometry. In an effort to incorporate quantitative structural information in bone analysis, Durand and Rüegsegger (24) developed a high-resolution mode for their QCT system for peripheral measuring sites to obtain images with high-contrast resolution of 0.25 mm and slice thickness of 1.3 mm. In their in vivo study they were able to show that the coefficient of variation of the structural properties was less than 5% in repetitive measurements. The reproducibility was assessed by measuring 3 tomograms 3 times of the distal radius of the same volunteer in time intervals of 3 months. Before analysis the measurements were repositioned with respect to rotational and translational shifts. All nine measurements were processed identically to assess the structural properties using a run-length method. Chevalier et al. (25) demonstrated the use of a morphologic analysis of CT images as a predictor of the trabecular network in an in vivo study of 165 normal and osteoporotic women. They measured the length of the network and the number of discontinuities found in the images of lumbar vertebrae with a slice thickness of 1.5 mm. Using this approach they were able to separate normal subjects from osteoporotic subjects independently of BMD. Although the results from those studies showed a correlation between bone structure and bone strength as an index for fracture risk or osteoporosis, it was not possible to fully explain the mechanical behavior of bone without taking into consideration the 3D nature of bone architecture (4). Basically the same limitations apply as mentioned earlier for conventional histomorphometry, for which Schenk and Olah (7) reported that it is only under certain circumstances that 3D results can be extracted from 2D measurements. Noninvasive bone biopsy To assess the 3D trabecular microstructure of intact bones, Müller et al. (26) introduced the concept of noninvasive bone biopsy, an in vivo method to assess and analyze volumetric datasets based on 3D high-resolution quantitative computed tomography (3D QCT). By means of 3D QCT it became possible for the first time to assess both apparent density and 3D trabecular microstructure of intact bones in a single measurement. These noninvasive bone biopsies can be processed nondestructively and, even more importantly, repetitively in either two or three dimensions. Data acquisition For data acquisition, a new system of QCT imaging of the forearm was used (27) including a 2D detector array (10 × 16 channels) in combination with a 0.2 × 10 mm line focus x-ray tube, which allowed simultaneous assessment of 10 tomographic images in each measurement cycle. The actual in vivo measurement protocol included the acquisition of a 3D stack of 60 high-resolution CT slices (6 × 10 images) in the distal end of the radius as illustrated in Figure 2. For 3D data acquisition, the CT settings used were as follows: effective energy, 50 keV; slice thickness, 0.28 mm; field of view, 85.0 mm; pixel matrix, 512 × 512; and pixel size, 0.17 mm. To obtain cubic voxels, the consecutive cross-sectional slices were measured in steps of 0.17 mm in the axial direction.FIG. 2.: In vivo measurement site is based on a low-dose digital radiogram (scout view) of the forearm performed prior to each CT measurement. Images are measured in increments of 170 μm, resulting in a total observation region of 10 mm.Data segmentation Data segmentation involved a two-level approach. On the first level, the VOI representing the raw data was defined (Fig. 3). Size and position of the VOI are chosen by the operator. In this case, the chosen VOI corresponded to a processing volume of 8.5 × 8.5 × 8.5 mm3. The position of the volume within the array was defined so that the VOI was always located within the area of the smallest cross-section in the stack of CT slices (typically the most proximal slice in the stack). On the second level, mineralized bone was separated from bone marrow and muscle tissue with the help of a 3D segmentation algorithm. Due to the irreversibility of initial mistakes, segmentation is a critical and crucial part in image analysis. The 3D segmentation algorithm is based on the analysis of directional derivatives. The derivatives are computed from a polynomial least-squares approximation of the original CT data. As a result, a binary volume including isolated trabecular plates and rods is obtained. The segmentation algorithm, which is optimized for noninvasively assessed trabecular bone structures, is discussed in detail elsewhere (28). Figure 3 shows the extracted structures in the VOI superimposed on the original tomographic images.FIG. 3.: Four cross-sectional images from the stack of 60 CT slices, from distal (upper left) to proximal (lower right). For baseline measurement, a three-dimensional data array has to be defined by the operator by selecting a VOI. In this case, the VOI within the dark gray boxes contains 50 × 50 × 50 voxels (8.5 × 8.5 × 8.5 mm3). Superimposed in light gray are the detected structural features identified by the 3D segmentation algorithm.Surface modeling For the visualization of 3D binary objects, a method described earlier by Lorensen and Cline (29) was followed. They developed an algorithm, called marching cubes, which makes it possible to triangulate the surface of any given voxel array very quickly. The marching cubes algorithm is directly applicable to rastered 3D data. The algorithm decides how a logical cube spawned by eight neighboring voxels is intersected by the surface. The resulting surface is a polygon represented by triangles. A voxel within a cube can either belong to the object or to the background. Depending on the voxel configurations within a cube, different triangulated surfaces will result from the intersection of the surface and the cube. After detecting the surface of the investigated cube in the discrete dataset, the algorithm marches on to the next cube. Using this simple divide-and-conquer approach, it was not only possible to obtain a 3D polygonal surface representation consisting exclusively of triangles, but also to smooth the surface effectively. After segmentation of the original CT data the selected VOI, also referred to as noninvasive bone biopsy, always represents a binary volume including the extracted trabecular plates and rods. Figure 4 shows an example of such a noninvasive bone biopsy in the distal radius. The volume, representing 21 × 20 × 20 voxels (3.6 × 3.4 × 3.4 mm3), was triangulated using the high-resolution mode of the extended marching cubes algorithm (28) resulting in 42,640 triangles. As can be seen in the figure, the central region of the distal radius is normally characterized by a structure of predominantly thick plates in the frontal plane, which are connected by thinner trabecular rods in the medial-lateral direction.FIG. 4.: CT image of cancellous bone from the distal radius showing a 3D representation of a volume of 3.6 × 3.4 × 3.4 mm3. Measurement was performed with a modified 3D QCT system with a high-contrast resolution of 250 μm.Volume modeling Because we are not only interested in surface properties of the bone architecture but also in the solid behavior, we would like to have means to build bone models consisting of volumetric elements. Such models find application in the assessment of the mechanical properties of bone, which is essential in the determination of the biomechanical competence of microstructural bone. To date, invasive and destructive methods such as compression and bending testing had been used to determine different mechanical properties such as bone strength and bone stiffness. To study the influence of apparent density and structural anisotropy on mechanical properties, different microstructural models of cancellous bone have been introduced. Most of these models are based on the general assumption that different types of cancellous bone have identical tissue properties but varying microscopic structures. McElhaney et al. (30) presented a porous block model in which the model predictions of bone modulus and bone strength in relationship to apparent porosity fitted the experimental data quite well. Gibson (31) used an analytic approach to predict the influence of different structural configurations on the mechanical behavior of cancellous bone. Four different configurations were distinguished for analysis that were basically defined by rodlike or platelike structures forming either open or closed cells. The results showed that the dependence of the elastic properties on the apparent density varied with the structural configuration used. Beaupre and Hayes (32) analyzed an open-celled structure representing a spherical void with the help of finite element analysis. Using uniaxial strain loading for both compression and shear, they constructed the apparent tensor of elasticity for an equivalent homogeneous material on a continuum level and compared the results with experimental measurements of bovine trabecular bone and natural foam. For the regular porous foam they found good agreement of the results, as would have been expected, but for trabecular bone the highly idealized model only predicted the elastic constants for regions exhibiting regular structures. Jensen et al. (33) proposed a semianalytic model for prediction of the mechanical properties of vertebral trabecular bone. For their model, which is based on thick vertical columns and thinner connecting horizontal struts, they introduced a measure of relative lattice disorder to account for the structural irregularities in trabecular bone. They demonstrated the apparent stiffness of a perfect cube lattice varied by a factor of 5 to 10 from a model with maximal irregularity, whereas the trabecular bone volume remained almost constant. These findings demonstrate the need for more physiologic models representing the trabecular microstructure in an accurate and detailed way. Williams and Lewis (9) proposed a 2D finite element model based on exact contour tracings from the transverse plane of a single tibial bone section. They presumed the 3D cancellous bone to be a highly oriented columnar structure. Different large-scale models of trabecular bone have been introduced, which have been analyzed using 3D finite element modeling (34–36). Müller and Rüegsegger (37) introduced a new automated mesh generator to create 3D finite element models directly based on the trabecular microstructure of selected CT subvolumes. Because of the complex shape of trabecular bone structures, common mesh generators would need extensive user interaction, which is time consuming. This is why an automatic mesh generator was developed with the aim to create finite element meshes of complex volumetric data quickly and without user interaction. The algorithm is based on the principal idea that the segmented volume describes a discrete dataset on a digital raster, allowing subdivision of the volume into small mesh areas defined by the voxel raster itself. Keyak et al. (38) used a similar approach to generate a mesh of cube-shaped isotropic elements to model an entire bone. The geometry of the bone was assessed by means of standard QCT. Using a typical element length of 4 mm the cube-shaped elements could not represent the surface geometry precisely; therefore, no attempt was made to model the bone surface or the structural architecture of the bone. Representative results, however, could be obtained for interior stress and strain distributions. Marks and Gardner (39) and Camacho et al. (40) showed that use of unsmoothed geometry results in a lack of convergence for elements with sharp geometric discontinuities on the surface; therefore, the results for the entire surface can be erroneous. Following the principal ideas of Lorensen and Cline, Müller and Rüegsegger (26) extended the triangular surface representation generated by the marching cubes algorithm to a tetrahedral volume representation. Like the original marching cubes algorithm the newly developed algorithm, also referred to as volumetric marching cubes (VOMAC), is applied on the 3D discrete dataset. Where the basic element of the marching cubes algorithm is a triangle, the basic element of the VOMAC algorithm is a tetrahedron. Instead of defining a triangle surface configuration for every eight-voxel-cube combination, a tetrahedron subvolume is assembled inside the enclosed volume. The described technique allows effective meshing of any digital structure for subsequent volumetric analysis. Although VOMAC was developed specifically for trabecular bone structures, the technique has been used to successfully mesh other complex-shaped anatomic structures, such as the human skull and brain as part of the Visible Human Project (Fig. 5) (41). Although the presented automated meshing procedure typically is very fast—a model with millions of elements can be created within minutes—subsequent mechanical finite element analysis often is computationally demanding, if not impossible, due to current size limitations in commercial finite element packages.FIG. 5.: Four solid finite elements models of a human skull (33 × 46 × 46 voxels) as generated with traditional voxel-based hexahedron meshing (A) and with progressive model smoothing with one (B), two (C), and three (D) smoothing iterations, respectively. From the images it becomes clear that it is possible to create very smooth and detailed volume models of bone structure using a fully automated approach. No user interaction is needed to generate these models.Three-dimensional quantitative morphometry Another way of quantitatively describing the changes in bone architecture with age or state of disease is calculation of morphometric indices, also referred to as quantitative bone morphometry. As mentioned earlier, structural properties of trabecular bone have been investigated in the past by examination of 2D sections of cancellous bone biopsies. Three-dimensional morphometric parameters then are derived from 2D images using stereologic methods (7,8). Whereas parameters such as bone volume density (BV/TV) and bone surface density (BS/TV) can be obtained directly from 2D images, a range of important parameters such as trabecular thickness (Tb.Th), trabecular separation (Tb.Sp), and trabecular number (Tb.N) are derived indirectly assuming a fixed structural model. Typically an ideal plate or rod model is used. Such assumptions are, however, critical because of the well-known fact that trabecular bone continuously changes its structure type as a result of remodeling. A deviation from the assumed model will lead to an unpredictable error of the indirectly derived parameters. This is particularly true in studies where we would like to follow the changes in bone structure in the course of age-related bone loss. In those cases, a predefined model assumption could easily overestimate or underestimate the effects of the bone atrophy depending on the assessed index. For these reasons and to take full advantage of the volumetric measuring technique, new methods, which make direct use of the 3D information, are required. To meet this demand, several new methods of 3D image processing have been presented, which make direct quantification of the actual architecture of trabecular bone possible (42–45). The definitions and methods used for calculation of the model-independent parameters have been developed and introduced for microstructural evaluation of trabecular bone as part of the BIOMED I study (19,46). In that study, metric and nonmetric parameters entirely based on direct 3D calculations were used. The volume of the trabeculae (BV) was calculated using tetrahedrons (see previous section) corresponding to the enclosed volume of the triangulated surface used for the surface area calculation (37,43). From this measure the relative bone volume (BV/TV) can be calculated, where the total volume (TV) is the volume of the whole examined sample. The bone surface area (BS) was calculated using surface triangulation of the binary data (28) based on marching cubes (29). The specific bone surface or bone surface-to-volume-ratio is given by BS/BV. In conventional stereology, these primary parameters are be used to derive other indices such as Tb.Th, Tb.Sp, or Tb.N based on the underlying model assumption. An even more indirect way to calculate these metric parameters is to derive the involved surface area indirectly, using methods such as mean intercept length or 2D perimeter estimation. Such methods were developed for 2D analysis of trabecular bone but nevertheless are used for analysis of 3D images (47). A previous study showed that such indirectly derived primary quantities might vary as much as 52% depending on the method used (48). A more direct approach to assess metric parameters from 3D images is based on measuring actual distances in 3D space. Such techniques do not rely on an assumed model type and therefore are not biased by eventual deviations of the actual structures from this model. In such a way, mean Tb.Th can be calculated directly and without an underlying model assumption by determining a local thickness at each voxel representing bone (44). The same method can be used to calculate the mean Tb.Sp by applying the thickness calculation to the nonbone parts of the 3D image. The separation is the thickness of the marrow cavities. The Tb.N is defined for the plate model as the number of plates per unit length. An alternative geometric interpretation can be formulated as the inverse distance between the midsection of the plates. For a general structure it would be possible to assess the mean distance between the mid axes of the structure and use the inverse of this measure to calculate the mean number of elements per unit length. The mid axes of the structure can be extracted from a binary 3D image using different techniques (49). In this implementation, 3D distance transformation to extract the geometric midpoints of the structure was used (44). To obtain a measure for mean distance between the points, the direct thickness method similar to Tb.Sp calculation was applied, i.e., the separation between the midaxes was assessed. In addition to the computation of the direct metric parameters, other nonmetric parameters can be calculated to describe the 3D nature of the bone structure. An estimation of the plate-rod characteristic of the structure can be achieved using the structure model index (SMI). SMI is calculated by a differential analysis of a triangulated surface of a structure (45). For an ideal plate-and-rod structure, the SMI value is 0 and 3, respectively. For a structure with both plates and rods of equal thickness, the value is between 0 and 3, depending on the volume ratio between rods and plates. Another parameter often used as an architectural index is the geometric anisotropy of a structure, which typically is determined using mean intercept length (MIL) measurements (50). MIL denotes the average distance between bone/marrow interfaces and is measured by tracing test lines in different directions in the examined VOI. From this measurement, an MIL tensor can be calculated by fitting the MIL values to an ellipsoid. The eigen values of this tensor then can be used to define the degree of anisotropy, which denotes the maximum to minimum MIL ratio. SIMULATION TECHNIQUES AND COMPUTATIONAL MODELS Simulation techniques have received considerable interest in recent years. This is partly due to the increasing availability of extensive computer resources on the researcher's desktop as well as to progress in the development of the simulation software tools. Here we concentrate on the simulation technique used for investigation of long-term effects of aging and bone adaptation. In the past, it was impossible to collect data over such a long period of time (years to decades) with existing equipment and in the analysis of mechanical bone systems, where experimental setups became too complex or would not allow study of mechanical phenomena on the microstructural level. Nondestructive testing of mechanical bone systems As stated in the Introduction, the ultimate goal of any bone measurement in patients is to estimate bone strength. The relationship between structural indices of cancellous bone and the anisotropic mechanical properties is well documented (5,47,51). An alternate approach to determine bone strength in vivo could consist of a noninvasive bone biopsy followed by a structural finite element analysis. Trabecular bone strength is determined by mechanical loads at the level of the trabeculae. As noted earlier, with the recent introduction of microstructural finite element models generated from computer reconstructions of trabecular bone, it now is possible to calculate loads at the microstructural or tissue level. These models have shown that predicted tissue stresses and strains in bone specimens can differ considerably from those estimated from apparent level stresses and strains for the material as a continuum (11,34,35). However, because the in situ loading conditions for these specimens are not exactly known, these models are not adequate for determination of realistic loading conditions in bone tissue. For this reason, there is a need for full-scale models including the cortical shell and realistic boundary conditions to model the musculoskeletal interface resulting in an improved prediction of individual bone strength as an indicator for fracture risk or osteoporosis. Van Rietbergen et al. (52) presented a large-scale microstructural model of an intact canine proximal femur to determine the tissue loading conditions in trabeculae. The objectives of that study were to supply reasonable estimates of these quantities for the canine femur and to compare predicted tissue stresses on the microstructural level to apparent stresses on the continuum level in a quantitative way. A 3D high-resolution computer reconstruction of the femur was made using a