Computer-aided method for quantification of cartilage thickness and volume changes using MRI: validation study using a synthetic model

The primary objective of this study was to develop a computer-aided method for the quantification of three-dimensional (3-D) cartilage changes over time in knees with osteoarthritis (OA). We introduced a local coordinate system (LCS) for the femoral and tibial cartilage boundaries that provides a standardized representation of cartilage geometry, thickness, and volume. The LCS can be registered in different data sets from the same patient so that results can be directly compared. Cartilage boundaries are segmented from 3-D magnetic resonance (MR) slices with a semi-automated method and transformed into offset-maps, defined by the LCS. Volumes and thickness are computed from these offset-maps. Further anatomical labeling allows focal volumes to be evaluated in predefined subregions. The accuracy of the automated behavior of the method was assessed, without any human intervention, using realistic, synthetic 3-D MR images of a human knee. The error in thickness evaluation is lower than 0.12 mm for the tibia and femur. Cartilage volumes in anatomical subregions show a coefficient of variation ranging from 0.11% to 0.32%. This method improves noninvasive 3-D analysis of cartilage thickness and volume and is well suited for in vivo follow-up clinical studies of OA knees.     

Unsupervised segmentation and quantification of anatomical knee features: data from the Osteoarthritis Initiative

This paper presents a fully automated method for segmenting articular knee cartilage and bone from in vivo 3-D dual echo steady state images. The magnetic resonance imaging (MRI) datasets were obtained from the Osteoarthritis Initiative (OAI) pilot study and include longitudinal images from controls and subjects with knee osteoarthritis (OA) scanned twice at each visit (baseline, 24 month). Initially, human experts segmented six MRI series. Five of the six resultant sets served as reference atlases for a multiatlas segmentation algorithm. The methodology created precise knee segmentations that were used to extract articular cartilage volume, surface area, and thickness as well as subchondral bone plate curvature. Comparison to manual segmentation showed Dice similarity coefficient (DSC) of 0.88 and 0.84 for the femoral and tibial cartilage. In OA subjects, thickness measurements showed test-retest precision ranging from 0.014 mm (0.6%) at the femur to 0.038 mm (1.6%) at the femoral trochlea. In the same population, the curvature test-retest precision ranged from 0.0005 mm(-1) (3.6%) at the femur to 0.0026 mm(-1) (11.7%) at the medial tibia. Thickness longitudinal changes showed OA Pearson correlation coefficient of 0.94 for the femur. In conclusion, the fully automated segmentation methodology produces reproducible cartilage volume, thickness, and shape measurements valuable for the study of OA progression.     

Limits on the accuracy of 3-D thickness measurement in magnetic resonance images--effects of voxel anisotropy

Measuring the thickness of sheet-like thin anatomical structures, such as articular cartilage and brain cortex, in three-dimensional (3-D) magnetic resonance (MR) images is an important diagnostic procedure. This paper investigates the fundamental limits on the accuracy of thickness determination in MR images. We defined thickness here as the distance between the two sides of boundaries measured at the subvoxel resolution, which are the zero-crossings of the second directional derivatives combined with Gaussian blurring along the normal directions of the sheet surface. Based on MR imaging and computer postprocessing parameters, characteristics for the accuracy of thickness determination were derived by a theoretical simulation. We especially focused on the effects of voxel anisotropy in MR imaging with variable orientation of sheet-like structure. Improved and stable accuracy features were observed when the standard deviation of Gaussian blurring combined with thickness determination processes was around square root of 2/2 times as large as the pixel size. The relation between voxel anisotropy in MR imaging and the range of sheet normal orientation within which acceptable accuracy is attainable was also clarified, based on the dependences of voxel anisotropy and the sheet normal orientation obtained by numerical simulations. Finally, in vitro experiments were conducted using an acrylic plate phantom and a resected femoral head to validate the results of theoretical simulation. The simulated thickness was demonstrated to be well-correlated with the actual in vitro thickness.     

Surface extraction and thickness measurement of the articular cartilage from MR images using directional gradient vector flow snakes

The accuracy of the surface extraction of magnetic resonance images of highly congruent joints with thin articular cartilage layers has a significant effect on the percentage errors and reproducibility of quantitative measurements (e.g., thickness and volume) of the articular cartilage. Traditional techniques such as gradient-based edge detection are not suitable for the extraction of these surfaces. This paper studies the extraction of articular cartilage surfaces using snakes, and a gradient vector flow (GVF)-based external force is proposed for this application. In order to make the GVF snake more stable and converge to the correct surfaces, directional gradient is used to produce the gradient vector flow. Experimental results show that the directional GVF snake is more robust than the traditional GVF snake for this application. Based on the newly developed snake model, an articular cartilage surface extraction algorithm is developed. Thickness is computed based on the surfaces extracted using the proposed algorithm. In order to make the thickness measurement more reproducible, a new thickness computation approach, which is called T-norm, is introduced. Experimental results show that the thickness measurement obtained by the new thickness computation approach has better reproducibility than that obtained by the existing thickness computation approaches.     

Web-Based Multilayer Viewing Interface for Knee Cartilage

Many adults suffer from osteoarthritis (OA) with the majority of people over 65 showing radiographic evidence of the disease. To carry out effective diagnosis and treatment, it is necessary to understand the progression of cartilage loss and study the effectiveness of therapeutic interventions. Hence, it is important to have accurate, fast diagnosis of the disease. In this paper, we describe a Web-based user interface that enables the direct viewing of 2-D and 3-D image data from the visceral and tissue levels of the biological continuum (i.e., the continuum comprising systems, viscera, tissue, cells, proteins, and genes)–-while preserving geometric integrity. This is achieved despite the fact that the data are from different modalities (i.e., magnetic resonance (MR) and light microscopy). The user interface was tested using image data acquired from a study of articular cartilage thickness in the porcine knee. The interface allows the clinician to view both MR and light microscopy images in an integrated manner—with the information linked geometrically.      

A Validated Model of Calf Compression and Deep Vessel Collapse During External Cuff Inflation

This paper presents a validated model of calf compression with an external pressure cuff as used for deep vein thrombosis. Magnetic resonance (MR) images of calf geometry were used to generate subject-specific finite-element (FE) models of the calf cross section. Ultrasound images of deep vessel collapse obtained through a water-filled cuff were used to validate model behavior. Calf/cuff pressure interface measurements were applied to the FE model and the resulting tissue deformation was compared with MR image in normal volunteers (three females, four males, age range 20-55) using two distinct cuffs. MR observations and the model results showed good qualitative agreement. A similar reduction in cross-sectional area of the posterior tibial veins was obtained under both symmetric compression (89%) and asymmetric compression (81%), but greater compression of the anterior tibial veins was achieved with symmetric compression. The need to account for the effective compressibility of the calf tissue suggests that external measurements of the calf tissue deformation will not accurately predict deep vessel collapse. These results have implications for the modification of venous haemodynamics by such systems and could help to improve cuff design.     

Learning active shape models for bifurcating contours

Statistical shape models are often learned from examples based on landmark correspondences between annotated examples. A method is proposed for learning such models from contours with inconsistent bifurcations and loops. Automatic segmentation of tibial and femoral contours in knee X-ray images is investigated as a step towards reliable, quantitative radiographic analysis of osteoarthritis for diagnosis and assessment of progression. Results are presented using various features, the Mahalanobis distance, distance weighted K-nearest neighbours, and two relevance vector machine-based methods as quality of fit measure.     

Monitoring osteoarthritis in the rat model using optical coherence tomography

OBJECTIVE: A need exists for an animal model to assess therapeutics for osteoarthritis (OA) without sacrificing the animal. Our goal is to assess the progression of experimentally induced osteoarthritis in the rat knee joint by monitoring articular cartilage thickness, surface abnormalities, and collagen organization using a new technology known as optical coherence tomography (OCT). DESIGN: OA was generated in Wistar Hanover rats via injection of sodium iodoacetate into the left articular joint of the knee while normal saline was injected as a control in the contralateral right knee. Rats were sacrificed at 1-, 2-, 3-, 4-, and 8-week intervals and the knee joints were subsequently harvested and imaged using normal and polarization sensitive OCT (PS-OCT). Treated knees were compared to normal counterparts in the contralateral leg. Following imaging, knees underwent both routine histological processing and picrosirus staining for organized collagen. RESULTS: OCT images indicate that injection of sodium iodoacetate resulted in a progressive decrease in cartilage thickness and loss of the bone-cartilage interface which correlated with histology. In addition, PS-OCT was able to detect collagen disorganization, an early indicator of OA. CONCLUSIONS: The use of OCT in combination with the induction of OA in rats is a promising new animal model for assessing articular changes with the goal of monitoring therapeutics longitudinally. Future work will extend the model to in vivo assessments.     

Vibration arthrometry in patients with knee joint disorders

Physiological patellofemoral crepitus (PPC) is the vibration signal produced by the knee joint during slow motion (less than 5 degrees per second), which can be measured by vibration arthrometry (VAM). By using the autoregressive (AR) model for the PPC signals of patients with knee osteoarthritis, the study analyzes the PPC signals to evaluate the condition of patellar-femoral joint cartilage. Accordingly, we can divide osteoarthritis into three types, type 1: the cartilage of patellar-femoral joint is intact, the osteoarthritis found in the femoral-tibial joint surface; type 2: degeneration occurs in the surface cartilage of both the femoral-tibial joint and the femoral trochlea, but not on the patellar surface; type 3: both patellar-femoral and femoral-tibial joints have osteoarthritis. For the analysis, the intraclass distance of AR coefficients and spectral power ratio of dominant poles are adopted. Based on the proposed method, two cases of type 1, six of type 2, and 28 of type 3 were found in 36 cases of knee osteoarthritis. This is in agreement with the operative findings. For comparison, the PPC signals of 10 subjects with normal knees (without pain or wound history) were also measured. The results of analysis of the 10 normal subjects were consistent and clearly differentiable from those of the osteoarthritis patients. Therefore, the proposed method is efficient for the analysis of the condition of patellar-femoral joint cartilage and VAM may become an alternative way of noninvasive diagnosis of knee osteoarthritis.     

Differences between pelvic skin and bone landmark identification in different seated positions on spinal-cord injured subjects

The purpose of this paper was to determine the differences between internal and external pelvic landmark locations in different seating positions. A computer tool developed for the registration of two series of images was used to obtain the internal geometry. First, images of the pelvis were acquired by magnetic resonance imaging (MRI) for each subject, in a supine position; internal landmarks were then identified on the images. Second, ultrasound images of the iliac crests were acquired in four seated positions. A registration algorithm was applied to obtain the transformation matrix between the two image reference systems. The MRI anatomical landmarks were, therefore, transferred into the ultrasound referential, to obtain their three-dimensional (3-D) location in the different seating positions. The external landmarks in those seated positions were identified with a 3-D digitizer. The results revealed that generally the internal and external coordinates of corresponding landmarks are statistically different. The differences are not only due to soft tissue thickness but also to different interpretations of the landmarks' locations between the supine and the seated postures. However, these differences generally did not affect significantly the accuracy with which orientation indexes can be estimated (pelvic tilt, obliquity, transverse rotation). Correlations were found between the internal and external coordinates, implying that linear regressions can be established.     

生物力学模型约束下的图像分割算法研究

引入基于生物力学约束的弹性可变形体模型,提出区别于传统Snake方法的内外能量构造方法,其中内能量取决于该弹性可变形体材料的物理特性,外能量是由图像等外部数据驱动,通过能量最小化过程达到平衡位置,即所要的分割结果。为了说明该算法的精确性和稳定性,分别在人工合成图上添加不同数量的噪声,并进行边界弱化。实验表明,该算法具有良好的分割效果。心脏核磁共振（MRI）图像分割的实验表明,该模型能有效地同时搜索到左心室的内外膜,解决了心外膜不易分割的难题。     

A Bayesian morphometry algorithm

Most methods for structure-function analysis of the brain in medical images are usually based on voxel-wise statistical tests performed on registered magnetic resonance (MR) images across subjects. A major drawback of such methods is the inability to accurately locate regions that manifest nonlinear associations with clinical variables. In this paper, we propose Bayesian morphological analysis methods, based on a Bayesian-network representation, for the analysis of MR brain images. First, we describe how Bayesian networks (BNs) can represent probabilistic associations among voxels and clinical (function) variables. Second, we present a model-selection framework, which generates a BN that captures structure-function relationships from MR brain images and function variables. We demonstrate our methods in the context of determining associations between regional brain atrophy (as demonstrated on MR images of the brain), and functional deficits. We employ two data sets for this evaluation: the first contains MR images of 11 subjects, where associations between regional atrophy and a functional deficit are almost linear; the second data set contains MR images of the ventricles of 84 subjects, where the structure-function association is nonlinear. Our methods successfully identify voxel-wise morphological changes that are associated with functional deficits in both data sets, whereas standard statistical analysis (i.e., t-test and paired t-test) fails in the nonlinear-association case.     

Automatic quantification of tibio-femoral contact area and congruity

We present methods to quantify the medial tibio- femoral (MTF) joint contact area (CA) and congruity index (CI) from low-field magnetic resonance imaging (MRI). Firstly, based on the segmented MTF cartilage compartments, we computed the contact area using the Euclidian distance transformation. The CA was defined as the area of the tibial superior surface and the femoral inferior surface that are less than a voxel width apart. Furthermore, the CI is computed point-by-point by assessing the first- and second-order general surface features over the contact area. Mathematically, it is the inverse distance between the local normal vectors (first-order features) scaled by the local normal curvatures (second-order features) along the local direction of principal knee motion in a local reference coordinate system formed by the directions of principal curvature and the surface normal vector. The abilities of the CA and the CI for diagnosing osteoarthritis (OA) at different levels (disease severity was assessed using the Kellgren and Lawrence Index, KL) were cross-validated on 288 knees at baseline. Longitudinal analysis was performed on 245 knees. The precision quantified on 31 scan-rescan pairs (RMS CV) for CA was 13.7% and for CI 7.5%. The CA increased with onset of the disease and then decreased with OA progression. The CI was highest in healthy and decreased with the onset of OA and further with disease progression. The CI showed an AUC of 0.69 (p < 0.0001) for separating KL = 0 and KL > 0. For separating KL < 1 or KL = 1 and KL > 1 knees, the AUC for CI was 0.73 (p < 0.0001). The CA demonstrated longitudinal responsiveness (SRM) at all stages of OA, whereas the CI did for advanced OA only. Eventually, the quantified CA and the CI might be suitable to help explaining OA onset, diagnosis of (early) OA, and measuring the efficacy of DMOADs in clinical trials.     

Mapping visual field with positron emission tomography bymathematical modeling of the retinotopic organization in the calcarinecortex

We developed an objective and quantitative method of mapping the human visual field with positron emission tomography (PET) and magnetic resonance imaging (MRI). The regional cerebral blood flow (rCBF) images were acquired with H₂¹⁵O-PET under visual fixation as well as under visual stimulation with flickering diodes arranged along the ring at 0°, 3°, 7°, 14°, 21°, or 29° from the fixation point. After coregistration of PET and MR images, we extracted the surface of the calcarine cortex from the MR images and unfolded it to a two-dimensional (2-D) elliptic plane, on which the activated PET images were superimposed. Then we transformed the unfolded calcarine cortex into the visual field coordinates using the complex logarithmic function proposed by Schwartz. A large individual variation was observed in the retinotopical organization as well as in the morphology of the calcarine cortex. The formula was valid only within 15° from the center of the visual field. The constant parameter in the formula was estimated to be 1.5. The cortical linear magnification factor was 12.1, 2.8, and 1.6 at 0, 5, and 10°, respectively. The areas of the central 10° and 40° in the visual field correspond to 50% and 81% of the calcarine surface, respectively     

An Iterative Extended Boundary Condition Method for Solving the Absorption Characteristics of Lossy Dielectric Objects of Large Aspect Ratios

The recently developed iterative extended boundary condition method (IEBCM) has been used to compute the internal fields induced in homogeneous, axisymmetric, lossy dielectric objects of large aspect ratios when exposed to incident planewave radiation. Calculations were made for both the E- and k-polarization cases. The computed results for a prolate spheroidal model of an average man are found to be accurate for frequencies up to 300 MHz, while the use of the popular EBCM [1] was found to be essentially restricted to frequencies less than 70 MHz for these models and exposure conditions. The applicability of the IEBCM to composite bodies has also been examined by studying the irradiation of a capped cylindrical object. This composite object was first partitioned into several overlapping spherical subregions, and, alternatively, into two spherical subregions overlapping with a central cylindrical subregion. Spherical harmonics were used to represent the internal fields in the spherical subregions, while cylindrical expansions were utilized in the cylindrical subregions. It is shown that the second partitioning scheme is more computationally efficient and thereby suggests that the basis functions used to represent the subregional fields should be compatible with the subregional geometry. The new IEBCM, therefore, is a very valuable procedure which provides the opportunity of using the mixed basis functions in the solution.     

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     

Segmenting articular cartilage automatically using a voxel classification approach

We present a fully automatic method for articular cartilage segmentation from magnetic resonance imaging (MRI) which we use as the foundation of a quantitative cartilage assessment. We evaluate our method by comparisons to manual segmentations by a radiologist and by examining the interscan reproducibility of the volume and area estimates. Training and evaluation of the method is performed on a data set consisting of 139 scans of knees with a status ranging from healthy to severely osteoarthritic. This is, to our knowledge, the only fully automatic cartilage segmentation method that has good agreement with manual segmentations, an interscan reproducibility as good as that of a human expert, and enables the separation between healthy and osteoarthritic populations. While high-field scanners offer high-quality imaging from which the articular cartilage have been evaluated extensively using manual and automated image analysis techniques, low-field scanners on the other hand produce lower quality images but to a fraction of the cost of their high-field counterpart. For low-field MRI, there is no well-established accuracy validation for quantitative cartilage estimates, but we show that differences between healthy and osteoarthritic populations are statistically significant using our cartilage volume and surface area estimates, which suggests that low-field MRI analysis can become a useful, affordable tool in clinical studies.     

Automatic detection of the boundary of the calcaneus fromultrasound parametric images using an active contour model; clinicalassessment

Presents a computerized method for automated detection of the boundary of the os calcis on in vivo ultrasound parametric images, using an active dynamic contour model. The initial contour, defined without user interaction, is an iso-contour extracted from the textural feature space. The contour is deformed through the action of internal and external forces, until stability is reached. The external forces, which characterize image features, are a combination of gray-level information and second-order textural features arising from local cooccurrence matrices. The broadband ultrasound attenuation (BUA) value is then averaged within the contour obtained. The method was applied to 381 clinical images. The contour was correctly detected in the great majority of the cases. For the short-term reproducibility study, the mean coefficient of variation was equal to 1.81% for BUA values and 4.95% for areas in the detected region. Women with osteoporosis had a lower BUA than age-matched controls (p=0.0005). In healthy women, the age-related decline was -0.45 dB/MHz/yr. In the group of healthy post-menopausal women, years since menopause, weight and age were significant predictors of BUA. These results are comparable to those obtained when averaging BUA values in a small region of interest     

Merging parametric active contours within homogeneous image regions for MRI-based lung segmentation

Inhaled hyperpolarized helium-3 (3He) gas is a new magnetic resonance (MR) contrast agent that is being used to study lung functionality. To evaluate the total lung ventilation from the hyperpolarized 3He MR images, it is necessary to segment the lung cavities. This is difficult to accomplish using only the hyperpolarized 3He MR images, so traditional proton (1H) MR images are frequently obtained concurrent with the hyperpolarized 3He MR examination. Segmentation of the lung cavities from traditional proton (1H) MRI is a necessary first step in the analysis of hyperpolarized 3He MR images. In this paper, we develop an active contour model that provides a smooth boundary and accurately captures the high curvature features of the lung cavities from the 1H MR images. This segmentation method is the first parametric active contour model that facilitates straightforward merging of multiple contours. The proposed method of merging computes an external force field that is based on the solution of partial differential equations with boundary condition defined by the initial positions of the evolving contours. A theoretical connection with fluid flow in porous media and the proposed force field is established. Then by using the properties of fluid flow we prove that the proposed method indeed achieves merging and the contours stop at the object boundary as well. Experimental results involving merging in synthetic images are provided. The segmentation technique has been employed in lung 1H MR imaging for segmenting the total lung air space. This technology plays a key role in computing the functional air space from MR images that use hyperpolarized 3He gas as a contrast agent.     

Three-dimensional anatomical model-based segmentation of MR brainimages through principal axes registration

Model-based segmentation and analysis of brain images depends on anatomical knowledge which may be derived from conventional atlases. Classical anatomical atlases are based on the rigid spatial distribution provided by a single cadaver. Their use to segment internal anatomical brain structures in a high-resolution MR brain image does not provide any knowledge about the subject variability, and therefore they are not very efficient in analysis. The authors present a method to develop three-dimensional computerized composite models of brain structures to build a computerized anatomical atlas. The composite models are developed using the real MR brain images of human subjects which are registered through the principal axes transformation. The composite models provide probabilistic spatial distributions, which represent the variability of brain structures and can be easily updated for additional subjects. The authors demonstrate the use of such a composite model of ventricular structure to help segmentation of the ventricles and cerebrospinal fluid of MR brain images. Here, a composite model of ventricles using a set of 22 human subjects is developed and used in a model-based segmentation of ventricles, sulci, and white matter lesions. To illustrate the clinical usefulness, automatic volumetric measurements on ventricular size and cortical atrophy for an additional eight alcoholics and 10 normal subjects were made. The volumetric quantitative results indicated regional brain atrophy in chronic alcoholics