MR phase imaging to quantify bone volume fraction: computer simulations and in vivo measurements

Magnetic resonance phase images can be used to assess trabecular bone by measuring the standard deviation of the phases in a region of interest. The standard deviation of regional phase measurements reflects the degree of magnetic field inhomogeneity caused by susceptibility differences between bone and marrow. A 3D computer model of trabecular bone was developed and then used to explore the influence of bone volume fraction and imaging parameters such as pixel size and slice width on the standard deviation of regional phase measurements. The results from these tests show that with appropriate selection of these parameters, phase spread strongly reflects variations in trabecular bone density (a correlation of R(2) = 0.98 with bone volume fraction between 0 and 10%). The technique was then applied in vivo on the radius of 25 patients who already had a bone density scan with peripheral quantitative tomography and a correlation between phase standard deviation and trabecular bone density was found (R(2) = 0.46).     

Comparison of Computer Simulated and Phantom Measured Phase Variance in the Study of Trabecular Bone

A new method using magnetic resonance phase images for the assessment of trabecular bone structure has recently been proposed. To test this method, a mathematical model is developed which calculates the phase distribution in gradient echo acquired phase images of a structure of Pyrex glass rods immersed in a copper sulfate solution. Several experiments were performed using a phantom built in the same way as the structure used in the mathematical model. The results from the model are compared with those from the phantom tests, and the influence of resolution and bone area fraction on the phase dispersion is studied. The good correlation between theoretical and experimental results shows that phase variance increases with increasing resolution and bone density. However, the dependence of variance on bone density is less prominent for large pixel sizes.     

Wavelet-based characterization of vertebral trabecular bone structure from magnetic resonance images at 3 T compared with micro-computed tomographic measurements

Trabecular bone structure and bone density contribute to the strength of bone and are important in the study of osteoporosis. Wavelets are a powerful tool in characterizing and quantifying texture in an image. The purpose of this study was to validate wavelets as a tool in computing trabecular bone thickness directly from gray-level images. To this end, eight cylindrical cores of vertebral trabecular bone were imaged using 3-T magnetic resonance imaging (MRI) and micro-computed tomography (microCT). Thickness measurements of the trabecular bone from the wavelet-based analysis were compared with standard 2D structural parameters analogous to bone histomorphometry (MR images) and direct 3D distance transformation methods (microCT images). Additionally, bone volume fraction was determined using each method. The average difference in trabecular thickness between the wavelet and standard methods was less than the size of 1 pixel size for both MRI and microCT analysis. A correlation (R) of .94 for microCT measurements and that of .52 for MRI were found for the bone volume fraction. Based on these results, we conclude that wavelet-based methods deliver results comparable with those from established MR histomorphometric measurements. Because the wavelet transform is more robust with respect to image noise and operates directly on gray-level images, it could be a powerful tool for computing structural bone parameters from MR images acquired using high resolution and thus limited signal scenarios.     

Relationship between cancellous bone induced magnetic field and ultrastructure in a rat ovariectomy model

The site-dependent variations in trabecular bone morphology were studied in the rat tibia by magnitude and phase difference three-dimensional nuclear magnetic resonance microscopy and image processing, and the implications of ovariectomy were evaluated. Specimens excised from the proximal tibial metaphysis in ovariectomized (n = 7) and intact control (n = 4) rats were imaged at 9.4T with their anatomic axes parallel to the direction of the magnetic field. An echo-offset 3D rapid spin-echo excitation pulse sequence was used to generate phase difference maps, from which the standard deviation of the phase difference, sigma(delta psi), was calculated. In addition, a fictitious rate constant, R2', was calculated from the slope of the exponential portion of the Fourier transform of the phase difference histogram. Trabecular bone volume fraction was also determined in the same volume of interest. The results show strong correlations between bone volume fraction and both sigma(delta psi) and R2', suggesting that these parameters could be useful for nondestructive assessment of trabecular bone volume.     

Characterization of trabecular bone structure from high-resolution magnetic resonance images using fuzzy logic

The purpose of this work was to apply fuzzy logic image processing techniques to characterize the trabecular bone structure with high-resolution magnetic resonance images. Fifteen ex vivo high-resolution magnetic resonance images of specimens of human radii at 1.5 T and 12 in vivo high-resolution magnetic resonance images of the calcanei of peri- and postmenopausal women at 3 T were obtained. Soft segmentation using fuzzy clustering was applied to MR data to obtain fuzzy bone volume fraction maps, which were then analyzed with three-dimensional (3D) fuzzy geometrical parameters and measures of fuzziness. Geometrical parameters included fuzzy perimeter and fuzzy compactness, while measures of fuzziness included linear index of fuzziness, quadratic index of fuzziness, logarithmic fuzzy entropy, and exponential fuzzy entropy. Fuzzy parameters were validated at 1.5 T with 3D structural parameters computed from microcomputed tomography images, which allow the observation of true trabecular bone structure and with apparent MR structural indexes at 1.5 T and 3 T. The validation was statistically performed with the Pearson correlation coefficient as well as with the Bland-Altman method. Bone volume fraction correlation values (r) were up to .99 (P<.001) with good agreements based on Bland-Altman analysis showing that fuzzy clustering is a valid technique to quantify this parameter. Measures of fuzziness also showed consistent correlations to trabecular number parameters (r>.85; P<.001) and good agreements based on Bland-Altman analysis, suggesting that the level of fuzziness in high-resolution magnetic resonance images could be related to the trabecular bone structure.     

In vivo multiple spin echoes imaging of trabecular bone on a clinical 1.5 T MR scanner

In vivo multiple spin echoes (MSE) images of bone marrow in trabecular bone were obtained for the first time on a clinical 1.5 T scanner. Despite of a reduced sensitivity of the MSE trabecular bone images with respect to the cerebral matter ones, it is possible to observe some features in the MSE trabecular bone images that may be useful in the diagnosis of osteopenic states. Two different CRAZED-type MSE imaging sequences based on spin-echo and EPI imaging modalities were applied in phantom and in vivo. Preliminary experimental results indicate that EPI imaging readout seems to conceal the MSE contrast correlated with pore dimension in porous media. However it is still possible to detect anisotropy effects related to the bone structure in MSE-EPI images. Some strategies are suggested to optimize the quality of MSE trabecular bone images.     

Prediction of backscatter coefficient in trabecular bones using a numerical model of three-dimensional microstructure

A model of ultrasonic backscattering for cancellous bone saturated by water is proposed. This model assumes that scattering is caused by the solid trabeculae and describes the cancellous bone as a weak scattering medium. The backscatter coefficient is related to the spatial Fourier transform of bone microarchitecture and to the density and compressibility fluctuations between the solid trabeculae and the saturating fluid. The computations of the model make use of three-dimensional numerical images of bone microarchitecture, obtained by tomographic reconstructions with a 10 microm spatial resolution. With this model, the predictions of the frequency dependence and of the magnitude of the backscatter coefficient are reasonably accurate. The theoretical predictions are compared to experimental data obtained on 19 specimens. An accuracy error of approximately 1 dB was found (difference between the averaged experimental values and theoretical predictions). One limit of the model may come from inaccurate values of trabecular bone characteristics needed for the computations (density and longitudinal velocity), which are yet to be precisely determined for human trabecular bone. However, the model is only slightly sensitive to variations of bone material properties. It was found that an accuracy error of 2.2 dB at maximum resulted from inaccurate a priori values of bone material properties. A computation of the elastic mean free path in the medium suggests that multiple scattering plays a minor role in the working frequency bandwidth (0.4-1.2 MHz). It follows from these results that a weak scattering medium model may be appropriate to describe scattering from trabecular bone.     

Unwrapping microcomputed tomographic images for measuring cortical osteolytic lesions in the 5T2 murine model of myeloma treated by bisphosphonate

Multiple myeloma is due to the proliferation of malignant plasma cells which increase the number of osteoclasts leading to trabecular and cortical bone osteolysis. The 5T2MM murine model reproduces the human disease and microcomputed tomography is a precise tool to investigate bone loss. Bisphosphonates (zoledronic acid or pamidronate) are used in preventing osteolysis. However, loss of cortical bone in not possible to quantify by histomorphometry on histological sections or microCT images.Osteolysis was studied in mice grafted with the 5THL subline to see if one drug was more active after 10 weeks. Mice were distributed into 4 groups: control, untreated, treated with pamidronate or with zoledronic acid. The left femurs were embedded undecalcified and sectioned at 7 μm. The right tibias and femurs were analyzed by microCT and trabecular morphometric parameters were obtained. Cortical bone osteolysis was analyzed by developing a new algorithm to unwrap microCT sections of the cortices, allowing measurement of the number of perforations, porosity and mean perforation area.The bisphosphonates had no significant effect on the tumor growth as evidence by the absence of effect on the M-protein level. Cortical perforations were evidenced on histological sections and their number seemed to be reduced by both bisphosphonates. MicroCT was used to quantify the trabecular bone: a bone loss was evidenced in the untreated myeloma group and both bisphosphonates appeared equal to preserve trabecular mass. However, the number and size of cortical perforations cannot be determined on 3D models. Unwrapping microCT images provided flat images allowing a precise determination of cortical perforations. Pamidronate did not reduce the number and size of cortical perforations but significantly reduced porosity. Zoledronic acid appeared significantly superior and considerably reduced all parameters.Unwrapping microCT image is a new method allowing the measurement of cortical perforations in bone malignancies, a parameter that cannot be measured correctly on 2D histological sections.     

基于水平集的牙齿牙槽骨图像分割

口腔锥形束计算机断层扫描（Cone Beam Computed Tomography,CBCT）图像中牙齿及牙槽骨的分割对骨性结构的三维重建提供了基础,是实现牙齿牙槽骨三维可视化的必要步骤.本文根据牙齿及牙槽骨特点,将一种改进的势阱函数与水平集模型结合,克服以往势阱函数在部分区域出现“停止演化”或“过快演化”的缺陷,并将其应用在对牙齿牙槽骨的分割当中.采用多次小方差高斯滤波叠加的方式对图像进行序贯滤波预处理,解决单一方差高斯滤波难以有效滤除CBCT图像中噪声的问题,为准确分割提供了条件;基于序列图像相邻两张图片中同一牙齿的轮廓变化不大这一特点,以当前层的分割结果作为下一层曲线演化的初始轮廓,使得用更少的迭代次数得到相同结果,从而提高分割速度.另外,本文还将该算法应用于口腔磁共振图像中,并成功对单颗牙齿进行了分割.     

Reproducibility of the quantitative assessment of cartilage morphology and trabecular bone structure with magnetic resonance imaging at 7 T

To assess the reproducibility of quantitative measurements of cartilage morphology and trabecular bone structure of the knee at 7 T, high-resolution sagittal spoiled gradient-echo images and high-resolution axial fully refocused steady-state free-precession (SSFP) images from six healthy volunteers were acquired with a 7-T scanner. The subjects were repositioned between repeated scans to test the reproducibility of the measurements. The reproducibility of each measurement was evaluated using the coefficient(s) of variation (CV). The computed CV were 1.13% and 1.55% for cartilage thickness and cartilage volume, respectively, and were 2.86%, 1.07%, 2.27% and 3.30% for apparent bone volume over total volume fraction (app.BV/TV), apparent trabecular number (app.Tb.N), apparent trabecular separation (app.Tb.Sp) and apparent trabecular thickness (app.Tb.Th), respectively. The results demonstrate that quantitative assessment of cartilage morphology and trabecular bone structure is reproducible at 7 T and motivates future musculoskeletal applications seeking the high-field strength's superior signal-to-noise ratio.     

Comparison of high-resolution MRI, optical microscopy and SEM for quantitation of trabecular architecture in the rat femur

Magnetic resonance imaging (MRI) has been used to analyze trabecular bone architecture in femur heads taken from adult Wistar rats. The aim of this study was to validate the use of MRI in assessing trabecular structure and morphology by comparing standard measures of bone morphology in the rat femur obtained from high resolution MRI with those obtained by conventional optical microscopy and by scanning electron microscopy (SEM). MR images were obtained on a Bruker 4.7 T micro-imaging system using a three-dimensional spin echo sequence with spatial resolution of 23 microm in-plane and a slice thickness of 39 microm. Optical images were obtained by de-calcifying the bone in EDTA and then sectioning 5-microm-thick slices. SEM images were obtained from bone embedded in epoxy resin with surface preparation by diamond polishing. Values of standard bone morphological parameters were compared and correlation coefficients between the MRI and the optical- and SEM-derived measures of morphology were calculated. Partial volume effects in MRI were minimized in this study by the use of very thin slices, yielding better agreement with optical- and SEM-derived measures of trabecular bone morphology than have been obtained in previous studies. Correlations between the MRI and optical data were significantly lower than those between the MRI and SEM data. Effects of de-calcification were also investigated. The results indicate that comparison of MRI with thin (de-calcified) optical images may be inherently flawed due to the destructive de-calcification and sectioning process used to prepare samples for the optical imaging.     

Measures of complexity for 3D image analysis of trabecular bone

Based on fractal properties and spatial auto-correlation, the measures of complexity lacunarity, Moran's I and Geary's C index are defined for 3D image analysis. Their abilities to investigate translational invariance, characteristic length scales, spatial correlation and shapes of 3D micro-structures are demonstrated on proto-typical examples. Finally, using these measures of complexity, 3D images of trabecular bone are analysed. The main findings are that the complexity of the trabecular structure decreases and the plate-like shapes of the trabeculae change to mainly rod-like shapes during bone loss. These results and the proposed measures could have a great impact for medicine and for space exploration.     

Robust visual correspondence computation using monogenic curvature phase based mutual information

Visual correspondence has been a major research topic in the fields of image registration, 3D reconstruction, and object tracking for some decades. However, due to the radiometric variations of images, conventional approaches fail to produce robust matching results. The traditional method of intensity-based mutual information performs very good for global variations between images, however, its performance degrades in the case of local radiometric variations. Monogenic curvature phase information, as an important local feature of the image, has the advantage of being robust against brightness variation. Hence, in this Letter, we propose an approach to compute the visual correspondence by coupling the advantages of mutual information and monogenic curvature phase. Experimental results demonstrate that the proposed approach can work robustly under radiometric variations.     

基于形态学的不完全性骨折CT图像裂痕定位

针对不完全性骨折的CT图像损伤位置不易明确定位的问题,提出了一种基于数学形态学的裂痕定位算法。为了从CT图像中获得准确的骨质区域,在CIE Lab均匀色彩空间对原始图像进行双边滤波去噪,利用最大类间方差法计算出最佳阈值,从而分离出骨质区域,采用数学形态学中的黑帽运算结合Canny边缘检测算子对裂痕位置进行精确定位。实验结果表明,能够自动提取并定位不完全性骨折CT图像的裂痕区域。算法易于实现,具有较强的鲁棒性和实用性,方便了医学影像诊断。     

Correlations of group velocity, phase velocity, and dispersion with bone density in bovine trabecular bone

The present study investigated the correlations of the group velocity, the phase velocity, and the velocity dispersion with the apparent bone density in bovine trabecular bone in vitro. The phase velocity exhibited the negative dispersion, consistent with the behavior in human trabecular bone. The group and the phase velocities were found to increase with increasing apparent bone density, respectively, exhibiting similar high correlations of r=0.94 and 0.96. The negative dispersion rate exhibited a decreasing dependence on the apparent bone density, with a significant correlation of r=-0.86.     

Experimental evaluation of a surface charge method for computing the induced magnetic field in trabecular bone.

The magnetic field induced in the pores of trabecular bone as a result of the susceptibility difference between bone and bone marrow was computed with the aid of magnetic surface charge models generated from images of trabecular bone specimens acquired at 78 and 63 microm resolution. The predicted field was compared with the values derived from 2D and 3D field maps obtained by echo-offset imaging techniques and excellent agreement was found between the two methods. Finally, from the slopes of regression between the experimental and computed fields, the absolute susceptibility of bone was nondestructively determined as -11.0 x 10(-6) (MKS), which is in close agreement with a reported value of -11.3 x 10(-6) obtained with powdered bone by means of a spectroscopic susceptibility matching technique (J. A. Hopkins and F. W. Wehrli, Magn. Reson. Med. 37, 494-500 (1997)).     

Dependence of threshold variations on the assessment of histomorphometric indices from computed microtomography using synchrotron radiation

In this work, the variation of threshold level for segmentation of tomographic image in a micron scale accomplished with synchrotron radiation was studied. Three different sites of rat femora were evaluated from computed microtomography performed at SYRMEP beamline of ELETTRA Synchrotron Laboratory with a resolution of 9 μm. An optimal threshold level was selected and then varied in two points up and down in steps of one point, corresponding to 0.39% per point. Histomorphometric indices were calculated directly from the three dimensional segmented images of trabecular microstructure. The results showed that histomorphometric indices presented small variations for all indices in all femur sites. The greater variation occurred for trabecular thickness (Tb.Th) [from ?2.84% to 2.99%] while the smaller one occurred for trabecular number (Tb.N) [?0.26% to 0.35].     

Modeling and analysis of multiple scattering of acoustic waves in complex media: application to the trabecular bone

The integral equations that describe scattering in the media with step-rise changing parameters have been numerically solved for the trabecular bone model. The model consists of several hundred discrete randomly distributed elements. The spectral distribution of scattering coefficients in subsequent orders of scattering has been presented. Calculations were carried on for the ultrasonic frequency ranging from 0.5 to 3 MHz. Evaluation of the contribution of the first, second, and higher scattering orders to total scattering of the ultrasounds in trabecular bone was done. Contrary to the approaches that use the μCT images of trabecular structure to modeling of the ultrasonic wave propagation condition, the 3D numerical model consisting of cylindrical elements mimicking the spatial matrix of trabeculae, was applied. The scattering, due to interconnections between thick trabeculae, usually neglected in trabecular bone models, has been included in calculations when the structure backscatter was evaluated. Influence of the absorption in subsequent orders of scattering is also addressed. Results show that up to 1.5 MHz, the influence of higher scattering orders on the total scattered field characteristic can be neglected while for the higher frequencies, the relatively high amplitude interference peaks in higher scattering orders clearly occur.     

Proton magnetic relaxation in bone marrow related to age and bone mineral density: low-resolution in vitro studies.

Detailed analysis of proton spin-spin and spin-lattice relaxation behaviors of the bone marrow in the presence of trabecular bone network was performed at low-resolution (B(0) = 0.496T) on rat vertebrae specimens deprived of spinal cord. Two groups of samples, from young and old healthy animals, were investigated before cellular necrosis had started. BMD measurements were carried out to quantify the expected age-related modifications of the trabecular bone network. 1H-MR measurements were also performed on the same samples, deprived of marrow and saturated with water, in order to control the validity of a possible interpretation of the marrow 1H-MR characteristics, in terms of marrow components, and to investigate the possible employment of these samples to study the trabecular bone network properties. We pointed out that: 1) a bimodal distribution of T(2i) and T(1i) values (distinguishing "fast" and "slow" relaxations) describes satisfactorily all the 1H-MR experimental decays; 2) age-related modifications of the trabecular bone network are marked by correlate variations of the BMD value and of the proton spin-spin relaxation rates in water saturated samples; 3) age-related modifications of marrow are underlined by variations of the average value of the "fast" T(2i) and of the "slow" T(1i) relaxation time distributions, which could be attributed to the marrow components different from the fat granules of the adipose cells.Our results suggest that studies in vitro on bone tissue, by 1H-MR techniques at low-resolution, may contribute to a better bone function characterization and, therefore, to a better clinical utilization of MRI techniques.     

Numerical simulation of wave propagation in cancellous bone

Numerical simulation of wave propagation is performed through 31 3D volumes of trabecular bone. These volumes were reconstructed from high synchrotron microtomography experiments and are used as the input geometry in a simulation software developed in our laboratory. The simulation algorithm accounts for propagation into both the saturating fluid and bone but absorption is not taken into account. We show that 3D simulation predicts phenomena observed experimentally in trabecular bones : linear frequency dependence of attenuation, increase of attenuation and speed of sound with the bone volume fraction, negative phase velocity dispersion in most of the specimens, propagation of fast and slow wave depending on the orientation of the trabecular network compared to the direction of propagation of the ultrasound. Moreover, the predicted attenuation is in very close agreement with the experimental one measured on the same specimens. Coupling numerical simulation with real bone architecture therefore provides a powerful tool to investigate the physics of ultrasound propagation in trabecular structures.