MR imaging and osteoporosis: fractal lacunarity analysis of trabecular bone.

We develop a method of magnetic resonance (MR) image analysis able to provide parameter(s) sensitive to bone microarchitecture changes in aging, and to osteoporosis onset and progression. The method has been built taking into account fractal properties of many anatomic and physiologic structures. Fractal lacunarity analysis has been used to determine relevant parameter(s) to differentiate among three types of trabecular bone structure (healthy young, healthy perimenopausal, and osteoporotic patients) from lumbar vertebra MR images. In particular, we propose to approximate the lacunarity function by a hyperbola model function that depends on three coefficients, alpha, beta, and gamma, and to compute these coefficients as the solution of a least squares problem. This triplet of coefficients provides a model function that better represents the variation of mass density of pixels in the image considered. Clinical application of this preliminary version of our method suggests that one of the three coefficients, beta, may represent a standard for the evaluation of trabecular bone architecture and a potentially useful parametric index for the early diagnosis of osteoporosis.     

Prediction of biomechanical properties of trabecular bone in MR images with geometric features and support vector regression

Whole knee joint MR image datasets were used to compare the performance of geometric trabecular bone features and advanced machine learning techniques in predicting biomechanical strength properties measured on the corresponding ex vivo specimens. Changes of trabecular bone structure throughout the proximal tibia are indicative of several musculoskeletal disorders involving changes in the bone quality and the surrounding soft tissue. Recent studies have shown that MR imaging also allows non-invasive 3-D characterization of bone microstructure. Sophisticated features like the scaling index method (SIM) can estimate local structural and geometric properties of the trabecular bone and may improve the ability of MR imaging to determine local bone quality in vivo. A set of 67 bone cubes was extracted from knee specimens and their biomechanical strength estimated by the yield stress (YS) [in MPa] was determined through mechanical testing. The regional apparent bone volume fraction (BVF) and SIM derived features were calculated for each bone cube. A linear multiregression analysis (MultiReg) and a optimized support vector regression (SVR) algorithm were used to predict the YS from the image features. The prediction accuracy was measured by the root mean square error (RMSE) for each image feature on independent test sets. The best prediction result with the lowest prediction error of RMSE = 1.021 MPa was obtained with a combination of BVF and SIM features and by using SVR. The prediction accuracy with only SIM features and SVR (RMSE = 1.023 MPa) was still significantly better than BVF alone and MultiReg (RMSE = 1.073 MPa). The current study demonstrates that the combination of sophisticated bone structure features and supervised learning techniques can improve MR-based determination of trabecular bone quality.     

Segmentation of cancellous bone from high-resolution computed tomography images: influence on trabecular bone measurements

The quantification of cancellous bone network from computed tomography (CT) images requires a segmentation step which is crucial and difficult because of the partial volume effect in CT images. In this paper, we present and evaluate a new approach for segmenting cancellous bone network from high-resolution CT (HRCT) slices. The idea is first to detect a skeleton from the crest lines of the structure and then to thicken it to extract the whole bone structure by satisfying local neighborhood constraints. The segmentation requires the adjustment of relative and not absolute parameters like most methods. We quantified the influence of these parameters on architectural measurements. Results were first validated by using a physical phantom and then examined on a series of 12 HRCT images of human lumbar vertebra of different ages. We demonstrated that the choice of segmentation parameters yielded important variability on architectural measurements (up to 20%), but less variability than a more commonly used approach. This stresses the importance of settle on the segmentation parameters for once, which is possible with the proposed method.     

Ex vivo assessment of trabecular bone structure from three-dimensional projection reconstruction MR micro-images

Magnetic resonance (MR) imaging has recently been proposed for assessing osteoporosis and predicting fracture risks. However, accurate acquisition techniques and image analysis protocols for the determination of the trabecular bone structure are yet to be defined. The aim of this study was to assess the potential of projection reconstruction (PR) MR microscopy in the analysis of the three-dimensional (3-D) architecture of trabecular bone and in the prediction of its biomechanical properties. High-resolution 3-D PR images (41 x 41 x 82 microm3 voxels) of 15 porcine trabecular bone explants were analyzed to determine the trabecular bone volume fraction (Vv), the mean trabecular thickness (Tb.Th), and the mean trabecular separation (Tb.Sp) using the method of directed secants. These parameters were then compared with those derived from 3-D conventional spin-echo microimages. In both cases, segmentation of the high-resolution images into bone and bone marrow was obtained using a spatial adaptive threshold. The contemporary inclusion of Vv, Tb.Th and 1/Tb.Sp in a multiple regression analysis significantly improved the prediction of Young's modulus (YM). The parameters derived from the PR spin-echo images were found to be stronger predictors of YM (R2 = 0.94, p = 0.004) than those derived from conventional spin-echo images (R2 = 0.79, p = 0.051). Our study indicates that projection reconstruction MR microscopy appears to be more accurate than the conventional Fourier transform method in the quantification of trabecular bone structure and in the prediction of its bioimechanical properties. The proposed PR approach should be readily adaptable to the in vivo MRI studies of osteoporosis.     

Automatic quantification of changes in bone in serial MR images of joints

Recent innovations in drug therapies have made it highly desirable to obtain sensitive biomarkers of disease progression that can be used to quantify the performance of candidate disease modifying drugs. In order to measure potential image-based biomarkers of disease progression in an experimental model of rheumatoid arthritis (RA), we present two different methods to automatically quantify changes in a bone in in-vivo serial magnetic resonance (MR) images from the model. Both methods are based on rigid and nonrigid image registration to perform the analysis. The first method uses segmentation propagation to delineate a bone from the serial MR images giving a global measure of temporal changes in bone volume. The second method uses rigid body registration to determine intensity change within a bone, and then maps these into a reference coordinate system using nonrigid registration. This gives a local measure of temporal changes in bone lesion volume. We detected significant temporal changes in local bone lesion volume in five out of eight identified candidate bone lesion regions, and significant difference in local bone lesion volume between male and female subjects in three out of eight candidate bone lesion regions. But the global bone volume was found to be fluctuating over time. Finally, we compare our findings with histology of the subjects and the manual segmentation of bone lesions.     

Correction of bias field in MR images using singularity function analysis

A new approach for correcting bias field in magnetic resonance (MR) images is proposed using the mathematical model of singularity function analysis (SFA), which represents a discrete signal or its spectrum as a weighted sum of singularity functions. Through this model, an MR image's low spatial frequency components corrupted by a smoothly varying bias field are first removed, and then reconstructed from its higher spatial frequency components not polluted by bias field. The thus reconstructed image is then used to estimate bias field for final image correction. The approach does not rely on the assumption that anatomical information in MR images occurs at higher spatial frequencies than bias field. The performance of this approach is evaluated using both simulated and real clinical MR images.     

Reversible compression of MR images

Methods for reversible coding can be classified according to the organization of the source model as either static, semi-adaptive, or adaptive. Magnetic resonance (MR) images have different statistical characteristics in the foreground and the background and separation is thus a promising path for reversible MR image compression. A new reversible compression method, based on static source models for foreground and background separately, is presented. The method is nonuniversal and uses contextual information to exploit the fact that entropy and bit rate are reduced by increasing the statistical order of the model. This paper establishes a realistic level of expectation regarding the bit rate in reversible MR image compression, in general, and the bit rate using static modeling, in particular. The experimental results show that compression using the new method can give bit rates comparable to the best existing reversible methods.     

Off-resonance correction of MR images

In magnetic resonance imaging (MRI), the spatial inhomogeneity of the static magnetic field can cause degraded images if the reconstruction is based on inverse Fourier transformation. This paper presents and discusses a range of fast reconstruction algorithms that attempt to avoid such degradation by taking the field inhomogeneity into account. Some of these algorithms are new, others are modified versions of known algorithms. Speed and accuracy of all these algorithms are demonstrated using spiral MRI.     

A comprehensive approach to the analysis of contrast enhanced cardiac MR images

Current magnetic resonance imaging (MRI) technology allows the determination of patient-individual coronary tree structure, detection of infarctions, and assessment of myocardial perfusion. Joint inspection of these three aspects yields valuable information for therapy planning, e.g., through classification of myocardium into healthy tissue, regions showing a reversible hypoperfusion, and infarction with additional information on the corresponding supplying artery. Standard imaging protocols normally provide image data with different orientations, resolutions and coverages for each of the three aspects, which makes a direct comparison of analysis results difficult. The purpose of this work is to develop methods for the alignment and combined analysis of these images. The proposed approach is applied to 21 datasets of healthy and diseased patients from the clinical routine. The evaluation shows that, despite limitations due to typical MRI artifacts, combined inspection is feasible and can yield clinically useful information.     

Knowledge-based interpretation of MR brain images

The authors have developed a method for fully automated segmentation and labeling of 17 neuroanatomic structures such as thalamus, caudate nucleus, ventricular system, etc. in magnetic resonance (MR) brain images. The authors' method is based on a hypothesize-and-verify principle and uses a genetic algorithm (GA) optimization technique to generate and evaluate image interpretation hypotheses in a feedback loop. The authors' method was trained in 20 individual T1-weighted MR images. Observer-defined contours of neuroanatomic structures were used as a priori knowledge. The method's performance was validated in eight MR images by comparison to observer-defined independent standards. The GA-based image interpretation method correctly interpreted neuroanatomic structures in all images from the test set. Computer-identified and observer-defined neuroanatomic structure areas correlated very well (r=0.99, y=0,95x-2.1). Border positioning errors were small, with a root mean square (rms) border positioning error of 1.5+/-0.6 pixels. The authors' GA-based image interpretation method represents a novel approach to image interpretation and has been shown to produce accurate labeling of neuroanatomic structures in a set of MR brain images.     

The information content of MR images

The theoretical information content, defined by C.E. Shannon (1948), is proposed as an objective measure of MR (magnetic resonance) image quality. This measure takes into account the contrast-to-noise ratio (CNR), scan resolution, and field of view. It is used to derive an optimum in the tradeoff problem between image resolution and CNR, and as a criterion to assess the usefulness of high-resolution (512(2)) MR images. The result tells that for a given total acquisition time, an optimum value of the resolution can be found. This optimum is very broad. To apply Shannon's theory on information constant to MR images, a model for the spatial spectral power density of these images is required. Such a model has been derived from experimental observations of ordinary MR images, as well as from theoretical considerations.     

Morphometric analysis of white matter lesions in MR images: method and validation

The analysis of MR images is evolving from qualitative to quantitative. More and more, the question asked by clinicians is how much and where, rather than a simple statement on the presence or absence of abnormalities. The authors present a study in which the results obtained with a semiautomatic, multispectral segmentation technique are quantitatively compared to manually delineated regions. The core of the semiautomatic image analysis system is a supervised artificial neural network classifier augmented with dedicated preand postprocessing algorithms, including anisotropic noise filtering and a surface-fitting method for the correction of spatial intensity variations. The study was focused on the quantitation of white matter lesions in the human brain. A total of 36 images from six brain volumes was analyzed twice by each of two operators, under supervision of a neuroradiologist. Both the intra- and interrater variability of the methods were studied in terms of the average tissue area detected per slice, the correlation coefficients between area measurements, and a measure of similarity derived from the kappa statistic. The results indicate that, compared to a manual method, the use of the semiautomatic technique not only facilitates the analysis of the images, but also has similar or lower intra- and interrater variabilities.     

Estimating the bias field of MR images

The authors propose a modification of Wells et al. (ibid., vol. 15, no. 4, p. 429-42, 1996) technique for bias field estimation and segmentation of magnetic resonance (MR) images. They show that replacing the class other, which includes all tissue not modeled explicitly by Gaussians with small variance, by a uniform probability density, and amending the expectation-maximization (EM) algorithm appropriately, gives significantly better results. The authors next consider the estimation and filtering of high-frequency information in MR images, comprising noise, intertissue boundaries, and within tissue microstructures. The authors conclude that post-filtering is preferable to the prefiltering that has been proposed previously. The authors observe that the performance of any segmentation algorithm, in particular that of Wells et al. (and the authors' refinements of it) is affected substantially by the number and selection of the tissue classes that are modeled explicitly, the corresponding defining parameters and, critically, the spatial distribution of tissues in the image. The authors present an initial exploration to choose automatically the number of classes and the associated parameters that give the best output. This requires the authors to define what is meant by “best output” and for this they propose the application of minimum entropy. The methods developed have been implemented and are illustrated throughout on simulated and real data (brain and breast MR)     

Learning-based deformable registration of MR brain images

This paper presents a learning-based method for deformable registration of magnetic resonance (MR) brain images. There are two novelties in the proposed registration method. First, a set of best-scale geometric features are selected for each point in the brain, in order to facilitate correspondence detection during the registration procedure. This is achieved by optimizing an energy function that requires each point to have its best-scale geometric features consistent over the corresponding points in the training samples, and at the same time distinctive from those of nearby points in the neighborhood. Second, the active points used to drive the brain registration are hierarchically selected during the registration procedure, based on their saliency and consistency measures. That is, the image points with salient and consistent features (across different individuals) are considered for the initial registration of two images, while other less salient and consistent points join the registration procedure later. By incorporating these two novel strategies into the framework of the HAMMER registration algorithm, the registration accuracy has been improved according to the results on simulated brain data, and also visible improvement is observed particularly in the cortical regions of real brain data.     

Volumetric analysis of MR images for glioma classification and their effect on brain tissues

This work aims to identify non-invasive quantitative parameters from three-dimensional brain magnetic resonance images in order: (1) to classify brain tumor (glioma) as low grade (LG) or high grade (HG) and (2) to analyze effect of tumor on brain gray matter (GM) and white matter (WM). In proposed model features were extracted from segmented tumor region based on its volume and shape for distinguishing the tumor grade. Statistical analysis revealed good correlation between segmented tumor volume and tumor grade. Various morphological parameters extracted from segmented tumor region were also significantly different for LG and HG cases (\(p<0.05\)). Also, for brain tumor patients a considerable variation in normalized GM (%GM) volume was obtained compared to normalized WM (%WM) volume for LG and HG cases. We also found that, relative to controls, there was higher effect on %GM and %WM volumes for HG glioma patients as compared to LG glioma patients. The experimental results show that proposed feature set achieves LG/HG classification with high accuracy using support vector machines classifier.     

Topological analysis of switched-capacitor networks

A topological approach to the analysis of s.c. networks is presented. A graph model is chosen and explicit formulae are subsequently derived for all transfer functions in the z-domain. A corresponding topological analysis program has been constructed, giving transfer functions which are analytically dependent on z and capacitance elements.     

Topological analysis of packet networks

The author describes a unified approach for the topological analysis of nonhierarchical and hierarchical packet networks. The approach differs from previous approaches in adopting an end-to-end mean delay objective and including a variety of practical routing constraints. These include limits on the number of paths allowed in a route, limits on the number of hops allowed in a path, and constraints due to prevalent virtual circuit implementations. For a broad range of networks, quantitative analysis based on this approach provides new insights into the complex relationships between network topology and routing and delay constraints. It is shown that the sole use of a network average delay criterion often leads to network designs that exhibit poor end-to-end mean delays for some node pairs, and that it is possible to configure networks that meet an end-to-end mean delay objective for every node pair at little or no additional cost     

Markov random field segmentation of brain MR images

Describes a fully-automatic three-dimensional (3-D)-segmentation technique for brain magnetic resonance (MR) images. By means of Markov random fields (MRF's) the segmentation algorithm captures three features that are of special importance for MR images, i.e., nonparametric distributions of tissue intensities, neighborhood correlations, and signal inhomogeneities. Detailed simulations and real MR images demonstrate the performance of the segmentation algorithm. In particular, the impact of noise, inhomogeneity, smoothing, and structure thickness are analyzed quantitatively. Even single-echo MR images are well classified into gray matter, white matter, cerebrospinal fluid, scalp-bone, and background. A simulated annealing and an iterated conditional modes implementation are presented     

Analysis of trabecular bone structure using Fourier transforms andneural networks

Hip fracture due to osteoporosis (OP) and hip osteoarthritis (OA) are both important causes of locomotor morbidity in the elderly population. In osteoporosis, bone mass gradually decreases until the skeleton is too fragile to support the body and a fracture occurs, typically in the femur, wrist or spine. In osteoarthritis, there is a proliferation of bone, leading to a stiffening of the tissue. Current clinical methods for assessment of bone changes in these disorders largely depend on assessing bone mineral density. However, this does not provide any information about bone structure, which is considered to be an equally important factor in assessing bone quality. This paper presents a novel approach for computer analysis of trabecular (or cancellous) bone structure. The technique uses a Fourier transform to generate a “spectral fingerprint” of an image. Principal components analysis is then applied to identify key features from the Fourier transform and this information is passed to a neural network for classification. Testing this on a series of 100 histological sections of trabecular bone from patients with OP and OA and a normal group correctly classified over 90% of the OP group with an overall accuracy of 77%-84%. Such high success rates on a small group suggest that this may provide a simple, but powerful, method for identifying alterations in bone structure     

Labeling of MR brain images using Boolean neural network

Presents a knowledge-based approach for labeling two-dimensional (2-D) magnetic resonance (MR) brain images using the Boolean neural network (BNN), which has binary inputs and outputs, integer weights, fast learning and classification, and guaranteed convergence. The approach consists of two components: a BNN clustering algorithm and a constraint satisfying Boolean neural network (CSBNN) labeling procedure. The BNN clustering algorithm is developed to initially segment an image into a number of regions. Then the segmented regions are labeled with the CSBNN, which is a modified version of BNN. The CSBNN uses a knowledge base that contains information on image-feature space and tissue models as constraints. The method is tested using sets of MR brain images. The regions of the different brain tissues are satisfactorily segmented and labeled. A comparison with the Hopfield neural network and the traditional simulated annealing method for image labeling is provided. The comparison results show that the CSBNN approach offers a fast, feasible, and reliable alternative to the existing techniques for medical image labeling.