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.     

Proton magnetic resonance microimaging of human trabecular bone

Proton magnetic resonance (1H magnetic resonance imaging (MRI)) images of human trabecular bone were acquired and discussed for two samples with different porosity. Three-dimensional 3D Spin Echo (3D SE) and Multi-Slice Multi-Echo (MSME) pulse sequences were examined. A very high slice resolution of (38 microm)2 was achieved (MSME). The intensity histograms were found useful for the characterization of the bone porosity. A spatial distribution of the spin-spin relaxation time T2 was monitored with the MSME pulse program. The work demonstrates the great potential of the proton MRI technique in the study of the trabecular bone morphology.     

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).     

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)).     

DTI of trabecular bone marrow

The development of NMR diffusion imaging and diffusion tensor imaging (DTI) has offered the possibility of studying the porous structures beyond anatomical imaging. In fact, random molecular motions, within tissue components, probe tissue microstructures. Up to now, the DTI method was mainly used to investigate cerebral morphology and study white matter diseases. In this study, it has been applied to trabecular bone marrow analysis to obtain structural information on spongy bone tissue. Our first results show that DTI could represent an important tool in studying the microstructural architecture of the trabecular bone as well as the microarchitecture of porous media.     

Ultrasound propagation in trabecular bone: A numerical study of the influence of microcracks

The accumulation of microdamage in trabecular bone tissue is suspected of being a predictive indicator of osteoporosis diagnosis. To quantify this microdamage, the Dynamic AcoustoElastic Testing (DAET) method measures the Time Of Flight (TOF) and amplitude variations of transmitted ultrasound (US) pulses, while the bone sample is submitted to a low frequency sinusoidal hydrostatic pressure (opening/closing of microcracks). However, DAET is both sensitive to viscoelastic properties changes and microcracks density. To verify the microcracks density contribution on DAET results, a numerical approach is proposed. Multliple configurations of microdamaged trabecular bone-tissue-like mesh have been simulated. A 2D pseudo-spectral time domain numerical model was then developed to simulate linear wave propagation in heterogeneous solids. The influence of the microcracks number and orientation on the US TOF was particularly investigated. Results are discussed and compared with experimental data obtained from DAET measurements in trabecular bone samples.     

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.     

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.     

Diffusion tensor imaging to study anisotropy in a particular porous system: the trabecular bone network

During the last decade, considerable effort has been invested into the development of diffusion tensor imaging (DTI) mainly used to investigate cerebral morphology. The aim of this paper is to review and to discuss our recent results about high magnetic field DTI application to study spongy bone tissue. Due to its peculiar properties, spongy bone represents a particular porous system sample. Strategies to perform DTI on porous systems and issues linked to DTI outcome interpretation are presented on the basis of our results concerning trabecular bone network characterization.     

A magnetic resonance imaging based method for measurement of tissue iron concentration in liver arterially embolized with ferrimagnetic particles designed for magnetic hyperthermia treatment of tumors

Rabbit liver was loaded with ferrimagnetic particles of gamma -Fe2 O3 (designed for magnetic hyperthermia treatment of liver tumors) by injecting various doses of a suspension of the particles into the hepatic artery in vivo. Proton transverse relaxation rate (R(2)) images of the livers in vivo, excised, and dissected were generated from a series of single spin-echo images. Mean R(2) values for samples of ferrimagnetic-particle-loaded liver dissected into approximate 1 cm cubes were found to linearly correlate with tissue iron concentration over the range from approximately 0.1 to at least 2.7 mg Fe/g dry tissue when measured at room temperature. Changing the temperature of ferrimagnetic-particle-loaded samples of liver from 1 degrees C to 37 degrees C had no observable effect on tissue R(2) values. However, a small but significant decrease in R(2) was found for control samples containing no ferrimagnetic material on raising the temperature from 1 degrees C to 37 degrees C. Both chemically measured iron concentrations and mean R(2) values for rabbit livers with implanted tumors tended to be higher than those measured for tumor-free liver. This study indicates that tissue R(2) measurement and imaging by nuclear magnetic resonance may have a useful role in magnetic hyperthermia therapy protocols for the treatment of liver cancer.     

Influence of age and osteoporosis on calcaneus trabecular bone structure: a preliminary in vivo MRI study by quantitative texture analysis

Recent developments in high-resolution MR imaging techniques have opened up new perspectives for structural characterization of trabecular bone by non-invasive methods. In this study, 3-D MR imaging was performed on 17 healthy volunteers and 6 osteoporotic patients. Two different MR sequences were used to evaluate the impact on MR acquisition on texture analysis results. Images were analyzed with four automated methods of texture analysis (grey level histogram, cooccurrence, runlength and gradient matrices) enabling quantitative analysis of grey level intensity and distribution within three different regions of interest (ROI). Texture analysis is not very frequently used since the interpretation of the large number of calculated parameters is difficult. We applied multiparametric data analyses such as principal component analysis (CFA) and hierarchical ascending classification (HAC) to determine the relevant parameters to differentiate between three sets of images (healthy young volunteers, healthy postmenopaused and osteoporotic patients). The results suggest that relevant texture information (depending on the ROI localization in the calcaneus) can be extracted from calcaneus MR images to evaluate osteoporosis and age effects on trabecular bone structure if strictly the same acquisition sequences are used for all patients' examination.     

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.     

Anisotropy of ultrasonic backscatter and attenuation from human calcaneus: implications for relative roles of absorption and scattering in determining attenuation

Although bone sonometry has been demonstrated to be useful in the diagnosis of osteoporosis, much remains to be learned about the processes governing the interactions between ultrasound and bone. In order to investigate these processes, ultrasonic attenuation and backscatter in two orientations were measured in 43 human calcaneal specimens in vitro at 500 kHz. In the mediolateral (ML) orientation, the ultrasound propagation direction is approximately perpendicular to the trabecular axes. In the anteroposterior (AP) orientation, a wide range of angles between the ultrasound propagation direction and trabecular axes is encountered. Average attenuation slope was 18% greater while average backscatter coefficient was 50% lower in the AP orientation compared with the ML orientation. Backscatter coefficient in both orientations approximately conformed to a cubic dependence on frequency, consistent with a previously reported model. These results support the idea that absorption is a greater component of attenuation than scattering in human calcaneal trabecular bone.     

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.     

Frequency-dependent attenuation and backscatter coefficients in bovine trabecular bone from 0.2 to 1.2 MHz

The frequency-dependent attenuation and backscatter coefficients were measured in 25 bovine femoral trabecular bone samples from 0.2 to 1.2 MHz. When the average attenuation coefficient was fitted to a nonlinear power law α(f)=α(0)+α(1)f(n), the exponent n was found to be 1.65. In contrast, the average backscatter coefficient was fitted to a power law η(f)=η(1)f(n) and the exponent n was measured as 3.25. The apparent bone density was significantly correlated with the parameter α(1) (0.2-0.7 MHz: r = 0.852, 0.6-1.2 MHz: r = 0.832) as well as the backscatter coefficient (0.5 MHz: r = 0.751, 1.0 MHz: r = 0.808).     

Study on the mean trabecular bone spacing based on fundamental frequency estimation method

Ultrasonic backscatter signals from the cancellous bone can be used to diagnose osteoporosis effectively due to its ability to provide the information of bone microstructure. Mean trabecular bone spacing(MTBS)is one of the important parameters for characterization of bone microstructure.This paper proposed a MTBS estimating method based on the fundamental frequency estimation,which was applied to backscatter signals from simulations, and in vitro bovine trabeculae.The estimated MTBS were compared with those of simplified inverse filter tracking(SIFT)algorithm and autoregressive(AR)cepstrum method.The results demonstrated that the proposed method is very robust for the MTBS estimation with more precise estimates and smaller estimated variance in the presence of a small signal-to-noise ratio (SNR),and a large scattering strength ratio of diffuse scatterers to regular ones.     

3D histomorphometric quantification of trabecular bones by computed microtomography using synchrotron radiation

Conventional bone histomorphometry is an important method for quantitative evaluation of bone microstructure. X-ray computed microtomography is a non-invasive technique, which can be used to evaluate histomorphometric indices in trabecular bones (BV/TV, BS/BV, Tb.N, Tb.Th, Tb.Sp). In this technique, 3D images are used to quantify the whole sample, differently from the conventional one, in which the quantification is performed in 2D slices and extrapolated for 3D case. In this work, histomorphometric quantification using synchrotron 3D X-ray computed microtomography was performed to quantify the bone structure at different skeletal sites as well as to investigate the effects of bone diseases on quantitative understanding of bone architecture. The images were obtained at Synchrotron Radiation for MEdical Physics (SYRMEP) beamline, at ELETTRA synchrotron radiation facility, Italy. Concerning the obtained results for normal and pathological bones from same skeletal sites and individuals, from our results, a certain declining bone volume fraction was achieved. The results obtained could be used in forming the basis for comparison of the bone microarchitecture and can be a valuable tool for predicting bone fragility.     

二次变换法估计骨小梁的间距

平均骨小梁间距作为松质骨微结构的重要表征参数,其值可作为诊断骨质疏松的重要参考信息。提出将二次变换法运用于骨小梁间距的估算,探究其运用于骨小梁间距估算的可行性。通过散射元仿真、时域有限差分法仿真和离体松质骨实验所得到松质骨背散射信号进行分析,同时以自回归倒谱法(AR倒谱法)、反向滤波-自回归倒谱法(反向滤波-AR倒谱法)、自适应滤波-自回归倒谱法(自适应滤波-AR倒谱法)和简易反向滤波跟踪(SIFT)算法作为对比方法进行分析,通过对比证明了其可行性和相比于其他方法的优越性。结果表明,不管是利用仿真实验还是牛胫骨的离体实验所得信号估算骨小梁间距,二次变换法比其他算法具有更强的测量稳定性和准确性。      

Quantification of trabecular structure in the distal femur using magnetic resonance phase imaging

A new approach for quantifying trabecular bone tissue using the phase images of a simple gradient-echo sequence is presented. The proposed method is based on the hypothesis that the differences in susceptibility between bone and bone marrow cause magnetic field (i.e., precession phase) variations between the image voxels. Phase images of the distal femur were obtained in vivo and characterised with the use of the phase variance. Computer simulations and experimental results indicate that the distribution of the phases varies with echo time and image resolution, as expected. Keeping these fixed, however, the phase variance is found to strongly reflect variations in trabecular structure.     

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.