Quantitative bone measurements using x-ray computed tomography with second-order correction

Two-component cortical bone and water, and trabecular bone and water models were used to study the beam hardening errors associated with computed tomography (CT) bone densitometry and sizing methods. Specimens used included a femur, humerus, radius, ulna, and vertebral bodies. A second-order correction algorithm was employed to improve the accuracy of these quantitative CT methods. Physical measurements of the bones were obtained to verify the CT results. Large discrepancies were found between the uncorrected and second-order corrected CT assessments of cortical bone density, trabecular bone density, water density within the medullary canal, total bone area, medullary canal area, and cortical area. The interosseous lucent streak was also quantitatively studied. Results showed that second-order correction significantly improved the accuracy of CT bone densitometry and sizing methods.     

Cone-beam computed tomography and microtomography for alveolar bone measurements

Purpose

To compare cone-beam computed tomography (CBCT) and microtomography (micro-CT) for alveolar bone measurements.

Methods

Forty teeth and alveolar bone blocks of five pigs were scanned on a micro-CT with a 9.05 μm pixel size, and on a CBCT device at 0.125 mm voxel size. One height and four thickness measurements were performed twice in standardized slices by two radiologists to verify reliability. Agreement between imaging methods was assessed by correlation coefficients, Bland–Altman plots, and the difference was tested by a Wilcoxon signed-rank test.

Results

Regarding intra- and interobserver agreements, all bone measurements presented excellent precision values for micro-CT, but interobserver agreement for CBCT presented good to moderate values. Bone height differed about 0.3 mm, but no statistically significant differences were found for the bone thickness measurements.

Conclusion

CBCT underestimated bone height. No statistically significant differences were found for bone thickness. Regions of thin bone tissue may not be visualized on CBCT images. There are risks of underestimating bone measurements with CBCT and assuming bone loss that does not exist clinically. Although the difference of the bone height measurement was small, the clinical relevance must be analyzed on how to interpret CBCT     

Performance of computed tomography for contrast agent concentration measurements with monochromatic x-ray beams: comparison of K-edge versus temporal subtraction

We investigated the performance of monochromatic computed tomography for the quantification of contrast agent concentrations. Two subtraction methods (K-edge subtraction and temporal subtraction) were evaluated and compared theoretically and experimentally in terms of detection limit, precision and accuracy. Measurements were performed using synchrotron x-rays with Lucite phantoms (10 cm and 17.5 cm in diameter) containing iodine or gadolinium solutions ranging from 50 microg ml(-1) to 5 mg ml(-1). The experiments were carried out using monochromators developed at the European Synchrotron Radiation Facility (ESRF) medical beamline. The phantoms were imaged either above and below the contrast agent K-edge, or before and after the addition of the contrast agent. Both methods gave comparable performance for phantoms less than 10 cm in diameter. For large phantoms, equivalent to a human head, the temporal subtraction is more suitable for detecting elements such as iodine, keeping a reasonable x-ray dose delivered to the phantom. A good agreement was obtained between analytical calculations, simulations and measurements. The beam harmonic content was taken into account in the simulations. It explains the performance degradation with high contrast agent concentrations. The temporal subtraction technique has the advantage of energy tunability and is well suited for imaging elements, such as iodine or gadolinium, in highly absorbing samples. For technical reasons, the K-edge method is preferable when the imaged organ is moving since the two measurements can be performed simultaneously, which is mandatory for obtaining a good subtraction.     

Accurate quantification of width and density of bone structures by computed tomography

In computed tomography (CT), the representation of edges between objects of different densities is influenced by the limited spatial resolution of the scanner. This results in the misrepresentation of density of narrow objects, leading to errors of up to 70% and more. Our interest is in the imaging and measurement of narrow bone structures, and the issues are the same for imaging with clinical CT scanners, peripheral quantitative CT scanners or micro CT scanners. Mathematical models, phantoms and tests with patient data led to the following procedures: (i) extract density profiles at one-degree increments from the CT images at right angles to the bone boundary; (ii) consider the outer and inner edge of each profile separately due to different adjacent soft tissues; (iii) measure the width of each profile based on a threshold at fixed percentage of the difference between the soft-tissue value and a first approximated bone value; (iv) correct the underlying material density of bone for each profile based on the measured width with the help of the density-versus-width curve obtained from computer simulations and phantom measurements. This latter curve is specific to a certain scanner and is not dependent on the densities of the tissues within the range seen in patients. This procedure allows the calculation of the material density of bone. Based on phantom measurements, we estimate the density error to be below 2% relative to the density of normal bone and the bone-width error about one tenth of a pixel size.     

Peripheral quantitative computed tomography in evaluation of bioactive glass incorporation with bone

This laboratory study examined the feasibility of non-invasive, in vivo peripheral quantitative computed tomography (pQCT) method in evaluation of bioactive glass incorporation with bone. An intramedullary defect model of the rat tibia was applied. The defect was filled with bioactive glass microspheres (diameter of 250-315 microm) or was left to heal without filling (empty controls). The results of the pQCT analysis were compared with those of histomorphometry. In the control defects, there was a good correlation (r2 = 0.776, p < 0.001) between the pQCT density of the intramedullary space and the amount of new bone measured by histomorphometry. In the defects filled with bioactive glass, the use of thresholding techniques of the applied pQCT system (Stratec XCT Research M) failed in separation of new bone formation and bioactive glass particles. However, detailed analysis of the pQCT attenuation profiles showed time-related changes which well matched with the histomorphometric results of new bone formation both in control and bioactive glass filled defects. The biphasic pQCT attenuation profiles of bioactive glass filled defects could be separated into two distinct peaks. In statistical analysis of various variables, the center (i.e. the value of attenuation) of the major attenuation peak was found to be the most significant indicator of the incorporation process. The center of the peak initially decreased (during the first 4 weeks of healing) and thereafter increased. These two phases probably reflect the primary resorption and reactivity of the bioactive glass microspheres in vivo followed by secondary new bone formation on their surfaces. Based on these results, pQCT-method seems to be suitable for in vivo follow-up of the bioactive glass incorporation processes. Although the imaging technique is not able to discriminate the individual microspheres from invading new bone unambiguously, the attenuation profiling seems to give adequate information about the state of the incorporation process. This information may help to establish non-invasive imaging techniques of synthetic bone substitutes for preclinical and clinical testing of their efficacy.     

Eigenvector decomposition of full-spectrum x-ray computed tomography

Energy-discriminated x-ray computed tomography (CT) data were projected onto a set of basis functions to suppress the noise in filtered back-projection (FBP) reconstructions. The x-ray CT data were acquired using a novel x-ray system which incorporated a single-pixel photon-counting x-ray detector to measure the x-ray spectrum for each projection ray. A matrix of the spectral response of different materials was decomposed using eigenvalue decomposition to form the basis functions. Projection of FBP onto basis functions created a de facto image segmentation of multiple contrast agents. Final reconstructions showed significant noise suppression while preserving important energy-axis data. The noise suppression was demonstrated by a marked improvement in the signal-to-noise ratio (SNR) along the energy axis for multiple regions of interest in the reconstructed images. Basis functions used on a more coarsely sampled energy axis still showed an improved SNR. We conclude that the noise-resolution trade off along the energy axis was significantly improved using the eigenvalue decomposition basis functions.     

Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography

We analyze the signal and noise propagation of differential phase-contrast computed tomography (PCT) compared with conventional attenuation-based computed tomography (CT) from a theoretical point of view. This work focuses on grating-based differential phase-contrast imaging. A mathematical framework is derived that is able to analytically predict the relative performance of both imaging techniques in the sense of the relative contrast-to-noise ratio for the contrast of any two materials. Two fundamentally different properties of PCT compared with CT are identified. First, the noise power spectra show qualitatively different characteristics implying a resolution-dependent performance ratio. The break-even point is derived analytically as a function of system parameters such as geometry and visibility. A superior performance of PCT compared with CT can only be achieved at a sufficiently high spatial resolution. Second, due to periodicity of phase information which is non-ambiguous only in a bounded interval statistical phase wrapping can occur. This effect causes a collapse of information propagation for low signals which limits the applicability of phase-contrast imaging at low dose.     

Assessment of bone tissue mineralization by conventional x-ray microcomputed tomography: comparison with synchrotron radiation microcomputed tomography and ash measurements

Assessment of bone tissue mineral density (TMD) may provide information critical to the understanding of mineralization processes and bone biomechanics. High-resolution three-dimensional assessment of TMD has recently been demonstrated using synchrotron radiation microcomputed tomography (SRmuCT); however, this imaging modality is relatively inaccessible due to the scarcity of SR facilities. Conventional desktop muCT systems are widely available and have been used extensively to assess bone microarchitecture. However, the polychromatic source and cone-shaped beam geometry complicate assessment of TMD by conventional muCT. The goal of this study was to evaluate muCT-based measurement of degree and distribution of tissue mineralization in a quantitative, spatially resolved manner. Specifically, muCT measures of bone mineral content (BMC) and TMD were compared to those obtained by SRmuCT and gravimetric methods. Cylinders of trabecular bone were machined from human femoral heads (n = 5), vertebrae (n = 5), and proximal tibiae (n = 4). Cylinders were imaged in saline on a polychromatic muCT system at an isotropic voxel size of 8 microm. Volumes were reconstructed using beam hardening correction algorithms based on hydroxyapatite (HA)-resin wedge phantoms of 200 and 1200 mg HA/cm3. SRmuCT imaging was performed at an isotropic voxel size of 7.50 microm at the National Synchrotron Light Source. Attenuation values were converted to HA concentration using a linear regression derived by imaging a calibration phantom. Architecture and mineralization parameters were calculated from the image data. Specimens were processed using gravimetric methods to determine ash mass and density, muCT-based BMC values were not affected by altering the beam hardening correction. Volume-averaged TMD values calculated by the two corrections were significantly different (p = 0.008) in high volume fraction specimens only, with the 1200 mg HA/cm3 correction resulting in a 4.7% higher TMD value. MuCT and SRmuCT provided significantly different measurements of both BMC and TMD (p < 0.05). In high volume fraction specimens, muCT with 1200 mg HA/cm3 correctionteg resulted in BMC and TMD values 16.7% and 15.0% lower, respectively, than SRmuCT values. In low volume fraction specimens, muCT with 1200 mg HA/cm3 correction resulted in BMC and TMD values 12.8% and 12.9% lower, respectively, than SRmuCT values. MuCT and SRmuCT values were well-correlated when volume fraction groups were considered individually (BMC R2 = 0.97-1.00; TMD R2 = 0.78-0.99). Ash mass and density were higher than the SRmuCT equivalents by 8.6% in high volume fraction specimens and 10.9% in low volume fraction specimens (p < 0.05). BMC values calculated by tomography were highly correlated with ash mass (ash versus muCT R2 = 0.96-1.00; ash versus SRmuCT R2 = 0.99-1.00). TMD values calculated by tomography were moderately correlated with ash density (ash versus muCT R2 = 0.64-0.72; ash versus SRmuCT R2 = 0.64). Spatially resolved comparisons highlighted substantial geometric nonuniformity in the muCT data, which were reduced (but not eliminated) using the 1200 mg HA/cm3 beam hardening correction, and did not exist in the SRmuCT data. This study represents the first quantitative comparison of muCT mineralization evaluation against SRnuCT and gravimetry. Our results indicate that muCT mineralization measures are underestimated but well-correlated with SRmuCT and gravimetric data, particularly when volume fraction groups are considered individually.     

Accuracy of high-resolution peripheral quantitative computed tomography for measurement of bone quality

The introduction of three-dimensional high-resolution peripheral in vivo quantitative computed tomography (HR-pQCT) (XtremeCT, Scanco Medical, Switzerland; voxel size 82 μm) provides a new approach to monitor micro-architectural bone changes longitudinally. The accuracy of HR-pQCT for three important determinants of bone quality, including bone mineral density (BMD), architectural measurements and bone mechanics, was determined through a comparison with micro-computed tomography (μCT) and dual energy X-ray absorptiometry (DXA). Forty measurements from 10 cadaver radii with low bone mass were scanned using the three modalities, and image registration was used for 3D data to ensure identical regions were analyzed.

The areal BMD of DXA correlated well with volumetric BMD by HR-pQCT despite differences in dimensionality (R² = 0.69), and the correlation improved when non-dimensional bone mineral content was assessed (R² = 0.80). Morphological parameters measured by HR-pQCT in a standard patient analysis, including bone volume ratio, trabecular number, derived trabecular thickness, derived trabecular separation, and cortical thickness correlated well with μCT measures (R² = 0.59–0.96). Additionally, some non-metric parameters such as connectivity density (R² = 0.90) performed well. The mechanical stiffness assessed by finite element analysis of HR-pQCT images was generally higher than for μCT data due to resolution differences, and correlated well at the continuum level (R² = 0.73).

The validation here of HR-pQCT against gold-standards μCT and DXA provides insight into the accuracy of the system, and suggests that in addition to the standard patient protocol, additional indices of bone quality including connectivity density and mechanical stiffness may be appropriate to include as part of a standard patient analysis for clinical monitoring of bone quality.     

Flow measurements with a high-speed computed tomography scanner

A high-speed computed tomography (CT) scanner with a scan time of 50 ms was used to measure flow in a phantom constructed to simulate both tissue and vessels. After a bolus injection of iodinated contrast medium, the phantom was scanned at a rate of up to 2 images/s. A gamma-variate curve was fit to the time-density data obtained from the inlet and outlet, as well as from the tissue-equivalent part of the phantom. Flow was then calculated using different curves and curve parameters according to the Stewart-Hamilton equation, the mean transit time, and a modification of the Sapirstein principle. Actual flow rates were assessed by timed sampling. The results demonstrated that high-speed CT can measure flow accurately by all these methods. Application of high-speed CT for flow measurements in experimental animals and patients is, therefore, promising. The limitations of each technique for clinical application are discussed.     

Bone-composition imaging using coherent-scatter computed tomography: assessing bone health beyond bone mineral density

Quantitative analysis of bone composition is necessary for the accurate diagnosis and monitoring of metabolic bone diseases. Accurate assessment of the bone mineralization state is the first requirement for a comprehensive analysis. In diagnostic imaging, x-ray coherent scatter depends upon the molecular structure of tissues. Coherent-scatter computed tomography (CSCT) exploits this feature to identify tissue types in composite biological specimens. We have used CSCT to map the distributions of tissues relevant to bone disease (fat, soft tissue, collagen, and mineral) within bone-tissue phantoms and an excised cadaveric bone sample. Using a purpose-built scanner, we have measured hydroxyapatite (bone mineral) concentrations based on coherent-scatter patterns from a series of samples with varying hydroxyapatite content. The measured scatter intensity is proportional to mineral density in true g/cm3. Repeated measurements of the hydroxyapatite concentration in each sample were within, at most, 2% of each other, revealing an excellent precision in determining hydroxyapatite concentration. All measurements were also found to be accurate to within 3% of the known values. Phantoms simulating normal, over-, and under-mineralized bone were created by mixing known masses of pure collagen and hydroxyapatite. An analysis of the composite scatter patterns gave the density of each material. For each composite, the densities were within 2% of the known values. Collagen and hydroxyapatite concentrations were also examined in a bone-mimicking phantom, incorporating other bone constituents (fat, soft tissue). Tomographic maps of the coherent-scatter properties of each specimen were reconstructed, from which material-specific images were generated. Each tissue was clearly distinguished and the collagen-mineral ratio determined from this phantom was also within 2% of the known value. Existing bone analysis techniques cannot determine the collagen-mineral ratio in intact specimens. Finally, to demonstrate the in situ potential of this technique, the mineralization state of an excised normal cadaveric radius was examined. The average collagen-mineral ratio of the cortical bone derived from material-specific images of the radius was 0.53+/-0.04, which is in agreement with the expected value of 0.55 for healthy bones.     

Improved reproducibility of high-resolution peripheral quantitative computed tomography for measurement of bone quality

A human high-resolution peripheral quantitative computed tomography scanner (HR-pQCT) (XtremeCT, Scanco Medical, Switzerland) capable of measuring three important indicators of bone quality (micro-architectural morphology, mineralization and mechanical stiffness) has been developed. The goal of this study was to evaluate the reproducibility of male and female HR-pQCT in vivo measurements, and elucidate the causes of error in these measurements through a comparison with in vitro measurements. The best possible short-term reproducibility was found using a set of 10 in vitro measurements without repositioning, and a set of 10 with repositioning. Subsequently, in vivo measurements were performed on 15 male and 15 female subjects at baseline and follow-ups of 1 week and 4 months to determine the short- and long-term reproducibility of the system. In addition to the 2D area matching method used in the standard evaluation protocol, a custom developed 3D registration method was used to find the common region between repeated scans. The best possible reproducibility without movement artifacts and repositioning error was less than 0.5%, while the reproducibility with repositioning error was less than 1.5%. The in vivo reproducibility of density (<1%), morphological (<4.5%) and stiffness (<3.5) measurements was consistently poorer than the reproducibility of cadaver measurements, presumably due to small movement artifacts and repositioning errors. Using 3D image registration, repositioning error was reduced on average by 23% and 8% for measurements of the radius and tibia sites, respectively. This study has provided bounds for the reproducibility of HR-pQCT to monitor bone quality longitudinally, and a basis for clinical study design to determine detectable changes.     

Monte Carlo simulation of a computed tomography x-ray tube

The dose delivered to patients during computed tomography (CT) exams has increased in the past decade. With the increasing complexity of CT examinations, measurement of the dose becomes more difficult and more important. In some cases, the standard methods, such as measurement of the computed tomography dose index (CTDI), are currently under question. One approach to determine the dose from CT exams is to use Monte Carlo (MC) methods. Since the patient geometry can be included in the model, Monte Carlo simulations are potentially the most accurate method of determining the dose delivered to patients. In this work, we developed a MC model of a CT x-ray tube. The model was validated with half-value layer (HVL) measurements and spectral measurements with a high resolution Schottky CdTe spectrometer. First and second HVL for beams without additional filtration calculated from the MC modelled spectra and determined from attenuation measurements differ by less than 2.5%. The differences between the first and second HVL for both filtered and non-filtered beams calculated from the MC modelled spectra and spectral measurements with the CdTe detector were less than 1.8%. The MC modelled spectra match the directly measured spectra. This works presents a first step towards an accurate MC model of a CT scanner.     

Spectrally resolving and scattering-compensated x-ray luminescence/fluorescence computed tomography

The nanophosphors, or other similar materials, emit near-infrared (NIR) light upon x-ray excitation. They were designed as optical probes for in vivo visualization and analysis of molecular and cellular targets, pathways, and responses. Based on the previous work on x-ray fluorescence computed tomography (XFCT) and x-ray luminescence computed tomography (XLCT), here we propose a spectrally-resolving and scattering-compensated x-ray luminescence/fluorescence computed tomography (SXLCT or SXFCT) approach to quantify a spatial distribution of nanophosphors (other similar materials or chemical elements) within a biological object. In this paper, the x-ray scattering is taken into account in the reconstruction algorithm. The NIR scattering is described in the diffusion approximation model. Then, x-ray excitations are applied with different spectra, and NIR signals are measured in a spectrally resolving fashion. Finally, a linear relationship is established between the nanophosphor distribution and measured NIR data using the finite element method and inverted using the compressive sensing technique. The numerical simulation results demonstrate the feasibility and merits of the proposed approach.     

Step-and-shoot data acquisition and reconstruction for cardiac x-ray computed tomography

Coronary artery imaging with x-ray computed tomography (CT) is one of the most recent advancements in CT clinical applications. Although existing "state-of-the-art" clinical protocols today utilize helical data acquisition, it suffers from the lack of ability to handle irregular heart rate and relatively high x-ray dose to patients. In this paper, we propose a step-and-shoot data acquisition protocol that significantly overcomes these shortcomings. The key to the proposed protocol is the large volume coverage (40 mm) enabled by the cone beam CT scanner, which allows the coverage of the entire heart in 3 to 4 steps. In addition, we propose a gated complementary reconstruction algorithm that overcomes the longitudinal truncation problem resulting from the cone beam geometry. Computer simulations, phantom experiments, and clinical studies were conducted to validate our approach.