Partial-volume Bayesian classification of material mixtures in MR volume data using voxel histograms

Quantifying lumbar paraspinal intramuscular fat: Accuracy and reliability of automated thresholding models

Background

The reported level of lumbar paraspinal intramuscular fat (IMF) in people with low back pain (LBP) varies considerably across studies using conventional T1- and T2-weighted magnetic resonance imaging (MRI) sequences. This may be due to the different thresholding models employed to quantify IMF. In this study we investigated the accuracy and reliability of established (two-component) and novel (three-component) thresholding models to measure lumbar paraspinal IMF from T2-weighted MRI.

Methods

In this cross-sectional study, we included MRI scans from 30 people with LBP (50% female; mean (SD) age: 46.3 (15.0) years). Gaussian mixture modelling (GMM) and K-means clustering were used to quantify IMF bilaterally from the lumbar multifidus, erector spinae, and psoas major using two and three-component thresholding approaches (GMM2C; K-means2C; GMM3C; and K-means3C). Dixon fat-water MRI was used as the reference for IMF. Accuracy was measured using Bland-Altman analyses, and reliability was measured using ICC3,1. The mean absolute error between thresholding models was compared using repeated-measures ANOVA and post-hoc paired sample t-tests (α = 0.05).

Results

We found poor reliability for K-means2C (ICC3,1 ≤ 0.38), moderate to good reliability for K-means3C (ICC3,1 ≥ 0.68), moderate reliability for GMM2C (ICC3,1 ≥ 0.63) and good reliability for GMM3C (ICC3,1 ≥ 0.77). The GMM (p < .001) and three-component models (p < .001) had smaller mean absolute errors than K-means and two-component models, respectively. None of the investigated models adequately quantified IMF for psoas major (ICC3,1 ≤ 0.01).

Conclusions

The performance of automated thresholding models is strongly dependent on the choice of algorithms, number of components, and muscle assessed. Compared to Dixon MRI, the GMM performed better than K-means and three-component performed better than two-component models for quantifying lumbar multifidus and erector spinae IMF. None of the investigated models accurately quantified IMF for psoas major. Future research is needed to investigate the performance of thresholding models in a more heterogeneous clinical dataset and across different sites and vendors.

NeSVoR: Implicit Neural Representation for Slice-to-Volume Reconstruction in MRI

Reconstructing 3D MR volumes from multiple motion-corrupted stacks of 2D slices has shown promise in imaging of moving subjects, e. g., fetal MRI. However, existing slice-to-volume reconstruction methods are time-consuming, especially when a high-resolution volume is desired. Moreover, they are still vulnerable to severe subject motion and when image artifacts are present in acquired slices. In this work, we present NeSVoR, a resolution-agnostic slice-to-volume reconstruction method, which models the underlying volume as a continuous function of spatial coordinates with implicit neural representation. To improve robustness to subject motion and other image artifacts, we adopt a continuous and comprehensive slice acquisition model that takes into account rigid inter-slice motion, point spread function, and bias fields. NeSVoR also estimates pixel-wise and slice-wise variances of image noise and enables removal of outliers during reconstruction and visualization of uncertainty. Extensive experiments are performed on both simulated and in vivo data to evaluate the proposed method. Results show that NeSVoR achieves state-of-the-art reconstruction quality while providing two to ten-fold acceleration in reconstruction times over the state-of-the-art algorithms.

Scan-Specific Generative Neural Network for MRI Super-Resolution Reconstruction

The interpretation and analysis of Magnetic resonance imaging (MRI) benefit from high spatial resolution. Unfortunately, direct acquisition of high spatial resolution MRI is time-consuming and costly, which increases the potential for motion artifact, and suffers from reduced signal-to-noise ratio (SNR). Super-resolution reconstruction (SRR) is one of the most widely used methods in MRI since it allows for the trade-off between high spatial resolution, high SNR, and reduced scan times. Deep learning has emerged for improved SRR as compared to conventional methods. However, current deep learning-based SRR methods require large-scale training datasets of high-resolution images, which are practically difficult to obtain at a suitable SNR. We sought to develop a methodology that allows for dataset-free deep learning-based SRR, through which to construct images with higher spatial resolution and of higher SNR than can be practically obtained by direct Fourier encoding. We developed a dataset-free learning method that leverages a generative neural network trained for each specific scan or set of scans, which in turn, allows for SRR tailored to the individual patient. With the SRR from three short duration scans, we achieved high quality brain MRI at an isotropic spatial resolution of 0.125 cubic mm with six minutes of imaging time for T2 contrast and an average increase of 7.2 dB (34.2%) in SNR to these short duration scans. Motion compensation was achieved by aligning the three short duration scans together. We assessed our technique on simulated MRI data and clinical data acquired from 15 subjects. Extensive experimental results demonstrate that our approach achieved superior results to state-of-the-art methods, while in parallel, performed at reduced cost as scans delivered with direct high-resolution acquisition.

Fast and High-Resolution Neonatal Brain MRI Through Super-Resolution Reconstruction From Acquisitions With Variable Slice Selection Direction

The brain of neonates is small in comparison to adults. Imaging at typical resolutions such as one cubic mm incurs more partial voluming artifacts in a neonate than in an adult. The interpretation and analysis of MRI of the neonatal brain benefit from a reduction in partial volume averaging that can be achieved with high spatial resolution. Unfortunately, direct acquisition of high spatial resolution MRI is slow, which increases the potential for motion artifact, and suffers from reduced signal-to-noise ratio. The purpose of this study is thus that using super-resolution reconstruction in conjunction with fast imaging protocols to construct neonatal brain MRI images at a suitable signal-to-noise ratio and with higher spatial resolution than can be practically obtained by direct Fourier encoding. We achieved high quality brain MRI at a spatial resolution of isotropic 0.4 mm with 6 min of imaging time, using super-resolution reconstruction from three short duration scans with variable directions of slice selection. Motion compensation was achieved by aligning the three short duration scans together. We applied this technique to 20 newborns and assessed the quality of the images we reconstructed. Experiments show that our approach to super-resolution reconstruction achieved considerable improvement in spatial resolution and signal-to-noise ratio, while, in parallel, substantially reduced scan times, as compared to direct high-resolution acquisitions. The experimental results demonstrate that our approach allowed for fast and high-quality neonatal brain MRI for both scientific research and clinical studies.

Hierarchical Image Semantics Using Probabilistic Path Propagations for Biomedical Research

Image segmentation is an important subtask in biomedical research applications, such as estimating the position and shape of a tumor. Unfortunately, advanced image segmentation methods are not widely applied in research applications as they often miss features, such as uncertainty communication, and may lack an intuitive approach for the use of the underlying algorithm. To solve this problem, this paper fuses a fuzzy and a hierarchical segmentation approach together, thus providing a flexible multiclass segmentation method based on probabilistic path propagations. By utilizing this method, analysts and physicians can map their mental model of image components and their composition to higher level objects. The probabilistic segmentation of higher order components is propagated along the user-defined hierarchy to highlight the potential of improvement resulting in each level of hierarchy by providing an intuitive representation. The effectiveness of this approach is demonstrated by evaluating our segmentations of biomedical datasets, comparing it to the state-of-the-art segmentation approaches, and an extensive user study.

Bayesian estimation of multicomponent relaxation parameters in magnetic resonance fingerprinting

PURPOSE

To estimate multiple components within a single voxel in magnetic resonance fingerprinting when the number and types of tissues comprising the voxel are not known a priori.

THEORY

Multiple tissue components within a single voxel are potentially separable with magnetic resonance fingerprinting as a result of differences in signal evolutions of each component. The Bayesian framework for inverse problems provides a natural and flexible setting for solving this problem when the tissue composition per voxel is unknown. Assuming that only a few entries from the dictionary contribute to a mixed signal, sparsity-promoting priors can be placed upon the solution.

METHODS

An iterative algorithm is applied to compute the maximum a posteriori estimator of the posterior probability density to determine the magnetic resonance fingerprinting dictionary entries that contribute most significantly to mixed or pure voxels.

RESULTS

Simulation results show that the algorithm is robust in finding the component tissues of mixed voxels. Preliminary in vivo data confirm this result, and show good agreement in voxels containing pure tissue.

CONCLUSIONS

The Bayesian framework and algorithm shown provide accurate solutions for the partial-volume problem in magnetic resonance fingerprinting. The flexibility of the method will allow further study into different priors and hyperpriors that can be applied in the model. Magn Reson Med 80:159-170, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

A Heavy Tailed Expectation Maximization Hidden Markov Random Field Model with Applications to Segmentation of MRI

A wide range of segmentation approaches assumes that intensity histograms extracted from magnetic resonance images (MRI) have a distribution for each brain tissue that can be modeled by a Gaussian distribution or a mixture of them. Nevertheless, intensity histograms of White Matter and Gray Matter are not symmetric and they exhibit heavy tails. In this work, we present a hidden Markov random field model with expectation maximization (EM-HMRF) modeling the components using the α-stable distribution. The proposed model is a generalization of the widely used EM-HMRF algorithm with Gaussian distributions. We test the α-stable EM-HMRF model in synthetic data and brain MRI data. The proposed methodology presents two main advantages: Firstly, it is more robust to outliers. Secondly, we obtain similar results than using Gaussian when the Gaussian assumption holds. This approach is able to model the spatial dependence between neighboring voxels in tomographic brain MRI.

Improving Separability of Structures with Similar Attributes in 2D Transfer Function Design

The 2D transfer function based on scalar value and gradient magnitude (SG-TF) is popularly used in volume rendering. However, it is plagued by the boundary-overlapping problem: different structures with similar attributes have the same region in SG-TF space, and their boundaries are usually connected. The SG-TF thus often fails in separating these structures (or their boundaries) and has limited ability to classify different objects in real-world 3D images. To overcome such a difficulty, we propose a novel method for boundary separation by integrating spatial connectivity computation of the boundaries and set operations on boundary voxels into the SG-TF. Specifically, spatial positions of boundaries and their regions in the SG-TF space are computed, from which boundaries can be well separated and volume rendered in different colors. In the method, the boundaries are divided into three classes and different boundary-separation techniques are applied to them, respectively. The complex task of separating various boundaries in 3D images is then simplified by breaking it into several small separation problems. The method shows good object classification ability in real-world 3D images while avoiding the complexity of high-dimensional transfer functions. Its effectiveness and validation is demonstrated by many experimental results to visualize boundaries of different structures in complex real-world 3D images.

Comparison of T1-weighted 2D TSE, 3D SPGR, and two-point 3D Dixon MRI for automated segmentation of visceral adipose tissue at 3 Tesla

OBJECTIVES

To evaluate and compare conventional T1-weighted 2D turbo spin echo (TSE), T1-weighted 3D volumetric interpolated breath-hold examination (VIBE), and two-point 3D Dixon-VIBE sequences for automatic segmentation of visceral adipose tissue (VAT) volume at 3 Tesla by measuring and compensating for errors arising from intensity nonuniformity (INU) and partial volume effects (PVE).

MATERIALS AND METHODS

The body trunks of 28 volunteers with body mass index values ranging from 18 to 41.2 kg/m² (30.02 ± 6.63 kg/m²) were scanned at 3 Tesla using three imaging techniques. Automatic methods were applied to reduce INU and PVE and to segment VAT. The automatically segmented VAT volumes obtained from all acquisitions were then statistically and objectively evaluated against the manually segmented (reference) VAT volumes.

RESULTS

Comparing the reference volumes with the VAT volumes automatically segmented over the uncorrected images showed that INU led to an average relative volume difference of -59.22 ± 11.59, 2.21 ± 47.04, and -43.05 ± 5.01 % for the TSE, VIBE, and Dixon images, respectively, while PVE led to average differences of -34.85 ± 19.85, -15.13 ± 11.04, and -33.79 ± 20.38 %. After signal correction, differences of -2.72 ± 6.60, 34.02 ± 36.99, and -2.23 ± 7.58 % were obtained between the reference and the automatically segmented volumes. A paired-sample two-tailed t test revealed no significant difference between the reference and automatically segmented VAT volumes of the corrected TSE (p = 0.614) and Dixon (p = 0.969) images, but showed a significant VAT overestimation using the corrected VIBE images.

CONCLUSION

Under similar imaging conditions and spatial resolution, automatically segmented VAT volumes obtained from the corrected TSE and Dixon images agreed with each other and with the reference volumes. These results demonstrate the efficacy of the signal correction methods and the similar accuracy of TSE and Dixon imaging for automatic volumetry of VAT at 3 Tesla.

Fully automated whole-head segmentation with improved smoothness and continuity, with theory reviewed

Individualized current-flow models are needed for precise targeting of brain structures using transcranial electrical or magnetic stimulation (TES/TMS). The same is true for current-source reconstruction in electroencephalography and magnetoencephalography (EEG/MEG). The first step in generating such models is to obtain an accurate segmentation of individual head anatomy, including not only brain but also cerebrospinal fluid (CSF), skull and soft tissues, with a field of view (FOV) that covers the whole head. Currently available automated segmentation tools only provide results for brain tissues, have a limited FOV, and do not guarantee continuity and smoothness of tissues, which is crucially important for accurate current-flow estimates. Here we present a tool that addresses these needs. It is based on a rigorous Bayesian inference framework that combines image intensity model, anatomical prior (atlas) and morphological constraints using Markov random fields (MRF). The method is evaluated on 20 simulated and 8 real head volumes acquired with magnetic resonance imaging (MRI) at 1 mm3 resolution. We find improved surface smoothness and continuity as compared to the segmentation algorithms currently implemented in Statistical Parametric Mapping (SPM). With this tool, accurate and morphologically correct modeling of the whole-head anatomy for individual subjects may now be feasible on a routine basis. Code and data are fully integrated into SPM software tool and are made publicly available. In addition, a review on the MRI segmentation using atlas and the MRF over the last 20 years is also provided, with the general mathematical framework clearly derived.

Boundary Aware Reconstruction of Scalar Fields

In visualization, the combined role of data reconstruction and its classification plays a crucial role. In this paper we propose a novel approach that improves classification of different materials and their boundaries by combining information from the classifiers at the reconstruction stage. Our approach estimates the targeted materials' local support before performing multiple material-specific reconstructions that prevent much of the misclassification traditionally associated with transitional regions and transfer function (TF) design. With respect to previously published methods our approach offers a number of improvements and advantages. For one, it does not rely on TFs acting on derivative expressions, therefore it is less sensitive to noisy data and the classification of a single material does not depend on specialized TF widgets or specifying regions in a multidimensional TF. Additionally, improved classification is attained without increasing TF dimensionality, which promotes scalability to multivariate data. These aspects are also key in maintaining low interaction complexity. The results are simple-to-achieve visualizations that better comply with the user's understanding of discrete features within the studied object.

Partial volume estimation in brain MRI revisited

We propose a fast algorithm to estimate brain tissue concentrations from conventional T1-weighted images based on a Bayesian maximum a posteriori formulation that extends the "mixel" model developed in the 90's. A key observation is the necessity to incorporate additional prior constraints to the "mixel" model for the estimation of plausible concentration maps. Experiments on the ADNI standardized dataset show that global and local brain atrophy measures from the proposed algorithm yield enhanced diagnosis testing value than with several widely used soft tissue labeling methods.

Segmentation-based partial volume correction for volume estimation of solid lesions in CT

In oncological chemotherapy monitoring, the change of a tumor's size is an important criterion for assessing cancer therapeutics. Measuring the volume of a tumor requires its delineation in 3-D. This is called segmentation, which is an intensively studied problem in medical image processing. However, simply counting the voxels within a binary segmentation result can lead to significant differences in the volume, if the lesion has been segmented slightly differently by various segmentation procedures or in different scans, for example due to the limited spatial resolution of computed tomography (CT) or partial volume effects. This variability limits the sensitivity of size measurements and thus of therapy response assessments and it can even lead to misclassifications. We present a fast, generic algorithm for measuring the volume of solid, compact tumors in CT that considers partial volume effects at the border of a given segmentation result. The algorithm is an extension of the segmentation-based partial volume analysis proposed by Kuhnigk for the volumetry of solid lung lesions , such that it can be applied to inhomogeneous lesions and lesions with inhomogeneous surroundings. Our generalized segmentation-based partial volume correction is based on a spatial subdivision of the segmentation result, from which the fraction of tumor for each voxel is computed. It has been evaluated on phantom data, 1516 lesion segmentation pairs (lung nodules, liver metastases and lymph nodes) as well as 1851 lung nodules from the LIDC-IDRI database. The evaluations of our algorithm show a more accurate estimation of the real volume and its ability to reduce inter- and intra-observer variability significantly for each entity. Overall, the variability (interquartile range) for phantom data is reduced by 49% ( p ≪ 0.001) and the variability between different readers is reduced by 28% ( p ≪ 0.001). The average computation time is 0.2 s.

Parameterization of the distribution of white and grey matter in MRI using the α-stable distribution

This work presents a study of the distribution of the grey matter (GM) and white matter (WM) in brain magnetic resonance imaging (MRI). The distribution of GM and WM is characterized using a mixture of α-stable distributions. A Bayesian α-stable mixture model for histogram data is presented and unknown parameters are sampled using the Metropolis-Hastings algorithm. The proposed methodology is tested in 18 real images from the MRI brain segmentation repository. The GM and WM distributions are accurately estimated. The α-stable distribution mixture model presented in this paper can be used as previous step in more complex MRI segmentation procedures using spatial information. Furthermore, due to the fact that the α-stable distribution is a generalization of the Gaussian distribution, the proposed methodology can be applied instead of the Gaussian mixture model, which is widely used in segmentation of brain MRI in the literature.

Automatic Tuning of Spatially Varying Transfer Functions for Blood Vessel Visualization

Computed Tomography Angiography (CTA) is commonly used in clinical routine for diagnosing vascular diseases. The procedure involves the injection of a contrast agent into the blood stream to increase the contrast between the blood vessels and the surrounding tissue in the image data. CTA is often visualized with Direct Volume Rendering (DVR) where the enhanced image contrast is important for the construction of Transfer Functions (TFs). For increased efficiency, clinical routine heavily relies on preset TFs to simplify the creation of such visualizations for a physician. In practice, however, TF presets often do not yield optimal images due to variations in mixture concentration of contrast agent in the blood stream. In this paper we propose an automatic, optimization-based method that shifts TF presets to account for general deviations and local variations of the intensity of contrast enhanced blood vessels. Some of the advantages of this method are the following. It computationally automates large parts of a process that is currently performed manually. It performs the TF shift locally and can thus optimize larger portions of the image than is possible with manual interaction. The method is based on a well known vesselness descriptor in the definition of the optimization criterion. The performance of the method is illustrated by clinically relevant CT angiography datasets displaying both improved structural overviews of vessel trees and improved adaption to local variations of contrast concentration.

Automatic segmentation of human facial tissue by MRI-CT fusion: a feasibility study

The aim of this study was to develop automatic image segmentation methods to segment human facial tissue which contains very thin anatomic structures. The segmentation output can be used to construct a more realistic human face model for a variety of purposes like surgery planning, patient specific prosthesis design and facial expression simulation. Segmentation methods developed were based on Bayesian and Level Set frameworks, which were applied on three image types: magnetic resonance imaging (MRI), computerized tomography (CT) and fusion, in which case information from both modalities were utilized maximally for every tissue type. The results on human data indicated that fusion, thickness adaptive and postprocessing options provided the best muscle/fat segmentation scores in both Level Set and Bayesian methods. When the best Level Set and Bayesian methods were compared, scores of the latter were better. Number of algorithm parameters (to be trained) and computer run time measured were also in favour of the Bayesian method.

Comparison of breast tissue measurements using magnetic resonance imaging, digital mammography and a mathematical algorithm

Women with mostly mammographically dense fibroglandular tissue (breast density, BD) have a four- to six-fold increased risk for breast cancer compared to women with little BD. BD is most frequently estimated from two-dimensional (2D) views of mammograms by a histogram segmentation approach (HSM) and more recently by a mathematical algorithm consisting of mammographic imaging parameters (MATH). Two non-invasive clinical magnetic resonance imaging (MRI) protocols: 3D gradient-echo (3DGRE) and short tau inversion recovery (STIR) were modified for 3D volumetric reconstruction of the breast for measuring fatty and fibroglandular tissue volumes by a Gaussian-distribution curve-fitting algorithm. Replicate breast exams (N = 2 to 7 replicates in six women) by 3DGRE and STIR were highly reproducible for all tissue-volume estimates (coefficients of variation <5%). Reliability studies compared measurements from four methods, 3DGRE, STIR, HSM, and MATH (N = 95 women) by linear regression and intra-class correlation (ICC) analyses. Rsqr, regression slopes, and ICC, respectively, were (1) 0.76-0.86, 0.8-1.1, and 0.87-0.92 for %-gland tissue, (2) 0.72-0.82, 0.64-0.96, and 0.77-0.91, for glandular volume, (3) 0.87-0.98, 0.94-1.07, and 0.89-0.99, for fat volume, and (4) 0.89-0.98, 0.94-1.00, and 0.89-0.98, for total breast volume. For all values estimated, the correlation was stronger for comparisons between the two MRI than between each MRI versus mammography, and between each MRI versus MATH data than between each MRI versus HSM data. All ICC values were >0.75 indicating that all four methods were reliable for measuring BD and that the mathematical algorithm and the two complimentary non-invasive MRI protocols could objectively and reliably estimate different types of breast tissues.

Volume visualization: a technical overview with a focus on medical applications

With the increasing availability of high-resolution isotropic three- or four-dimensional medical datasets from sources such as magnetic resonance imaging, computed tomography, and ultrasound, volumetric image visualization techniques have increased in importance. Over the past two decades, a number of new algorithms and improvements have been developed for practical clinical image display. More recently, further efficiencies have been attained by designing and implementing volume-rendering algorithms on graphics processing units (GPUs). In this paper, we review volumetric image visualization pipelines, algorithms, and medical applications. We also illustrate our algorithm implementation and evaluation results, and address the advantages and drawbacks of each algorithm in terms of image quality and efficiency. Within the outlined literature review, we have integrated our research results relating to new visualization, classification, enhancement, and multimodal data dynamic rendering. Finally, we illustrate issues related to modern GPU working pipelines, and their applications in volume visualization domain.

Simplified Computation for Nonparametric Windows Method of Probability Density Function Estimation

Recently, Kadir and Brady proposed a method for estimating probability density functions (PDFs) for digital signals which they call the Nonparametric (NP) Windows method. The method involves constructing a continuous space representation of the discrete space and sampled signal by using a suitable interpolation method. NP Windows requires only a small number of observed signal samples to estimate the PDF and is completely data driven. In this short paper, we first develop analytical formulae to obtain the NP Windows PDF estimates for 1D, 2D, and 3D signals, for different interpolation methods. We then show that the original procedure to calculate the PDF estimate can be significantly simplified and made computationally more efficient by a judicious choice of the frame of reference. We have also outlined specific algorithmic details of the procedures enabling quick implementation. Our reformulation of the original concept has directly demonstrated a close link between the NP Windows method and the Kernel Density Estimator.

Brain MRI segmentation with multiphase minimal partitioning: a comparative study

This paper presents the implementation and quantitative evaluation of a multiphase three-dimensional deformable model in a level set framework for automated segmentation of brain MRIs. The segmentation algorithm performs an optimal partitioning of three-dimensional data based on homogeneity measures that naturally evolves to the extraction of different tissue types in the brain. Random seed initialization was used to minimize the sensitivity of the method to initial conditions while avoiding the need for a priori information. This random initialization ensures robustness of the method with respect to the initialization and the minimization set up. Postprocessing corrections with morphological operators were applied to refine the details of the global segmentation method. A clinical study was performed on a database of 10 adult brain MRI volumes to compare the level set segmentation to three other methods: “idealized” intensity thresholding, fuzzy connectedness, and an expectation maximization classification using hidden Markov random fields. Quantitative evaluation of segmentation accuracy was performed with comparison to manual segmentation computing true positive and false positive volume fractions. A statistical comparison of the segmentation methods was performed through a Wilcoxon analysis of these error rates and results showed very high quality and stability of the multiphase three-dimensional level set method.

Component analysis approach to estimation of tissue intensity distributions of 3D images

Many segmentation algorithms in medical imaging rely on accurate modeling and estimation of tissue intensity probability density functions. Gaussian mixture modeling, currently the most common approach, has several drawbacks, such as reliance on a Gaussian model and iterative local optimization used to estimate the model parameters. It also does not take advantage of substantially larger amount of data provided by 3D acquisitions, which are becoming standard in clinical environment. We propose a novel and completely non-parametric algorithm to estimate the tissue intensity probabilities in 3D images. Instead of relying on traditional framework of iterating between classification and estimation, we pose the problem as an instance of a blind source separation problem, where the unknown distributions are treated as sources and histograms of image subvolumes as mixtures. The new approach performed well on synthetic data and real magnetic resonance imaging (MRI) scans of the brain, robustly capturing intensity distributions of even small image structures and partial volume voxels.

Spatial conditioning of transfer functions using local material distributions

In many applications of Direct Volume Rendering (DVR) the importance of a certain material or feature is highly dependent on its relative spatial location. For instance, in the medical diagnostic procedure, the patient's symptoms often lead to specification of features, tissues and organs of particular interest. One such example is pockets of gas which, if found inside the body at abnormal locations, are a crucial part of a diagnostic visualization. This paper presents an approach that enhances DVR transfer function design with spatial localization based on user specified material dependencies. Semantic expressions are used to define conditions based on relations between different materials, such as only render iodine uptake when close to liver. The underlying methods rely on estimations of material distributions which are acquired by weighing local neighborhoods of the data against approximations of material likelihood functions. This information is encoded and used to influence rendering according to the user's specifications. The result is improved focus on important features by allowing the user to suppress spatially less-important data. In line with requirements from actual clinical DVR practice, the methods do not require explicit material segmentation that would be impossible or prohibitively time-consuming to achieve in most real cases. The scheme scales well to higher dimensions which accounts for multi-dimensional transfer functions and multivariate data. Dual-Energy Computed Tomography, an important new modality in radiology, is used to demonstrate this scalability. In several examples we show significantly improved focus on clinically important aspects in the rendered images.

Automated brain tissue segmentation based on fractional signal mapping from inversion recovery Look-Locker acquisition

Most current automated segmentation methods are performed on T(1)- or T(2)-weighted MR images, relying on relative image intensity that is dependent on other MR parameters and sensitive to B(1) magnetic field inhomogeneity. Here, we propose an image segmentation method based on quantitative longitudinal magnetization relaxation time (T(1)) of brain tissues. Considering the partial volume effect, fractional volume maps of brain tissues (white matter, gray matter, and cerebrospinal fluid) were obtained by fitting the observed signal in an inversion recovery procedure to a linear combination of three exponential functions, which represents the relaxations of each of the tissue types. A Look-Locker acquisition was employed to accelerate the acquisition process. The feasibility and efficacy of this proposed method were evaluated using simulations and experiments. The potential applications of this method in the study of neurological disease as well as normal brain development and aging are discussed.

Topology-corrected segmentation and local intensity estimates for improved partial volume classification of brain cortex in MRI

In magnetic resonance imaging (MRI), accuracy and precision with which brain structures may be quantified are frequently affected by the partial volume (PV) effect. PV is due to the limited spatial resolution of MRI compared to the size of anatomical structures. Accurate classification of mixed voxels and correct estimation of the proportion of each pure tissue (fractional content) may help to increase the precision of cortical thickness estimation in regions where this measure is particularly difficult, such as deep sulci. The contribution of this work is twofold: on the one hand, we propose a new method to label voxels and compute tissue fractional content, integrating a mechanism for detecting sulci with topology preserving operators. On the other hand, we improve the computation of the fractional content of mixed voxels using local estimation of pure tissue intensity means. Accuracy and precision were assessed using simulated and real MR data and comparison with other existing approaches demonstrated the benefits of our method. Significant improvements in gray matter (GM) classification and cortical thickness estimation were brought by the topology correction. The fractional content root mean squared error diminished by 6.3% (p<0.01) on simulated data. The reproducibility error decreased by 8.8% (p<0.001) and the Jaccard similarity measure increased by 3.5% on real data. Furthermore, compared with manually guided expert segmentations, the similarity measure was improved by 12.0% (p<0.001). Thickness estimation with the proposed method showed a higher reproducibility compared with the measure performed after partial volume classification using other methods.

Measurement of cortical thickness from MRI by minimum line integrals on soft-classified tissue

Estimating the thickness of the cerebral cortex is a key step in many brain imaging studies, revealing valuable information on development or disease progression. In this work, we present a framework for measuring the cortical thickness, based on minimizing line integrals over the probability map of the gray matter in the MRI volume. We first prepare a probability map that contains the probability of each voxel belonging to the gray matter. Then, the thickness is basically defined for each voxel as the minimum line integral of the probability map on line segments centered at the point of interest. In contrast to our approach, previous methods often perform a binary-valued hard segmentation of the gray matter before measuring the cortical thickness. Because of image noise and partial volume effects, such a hard classification ignores the underlying tissue class probabilities assigned to each voxel, discarding potentially useful information. We describe our proposed method and demonstrate its performance on both artificial volumes and real 3D brain MRI data from subjects with Alzheimer's disease and healthy individuals.

Distribution-driven visualization of volume data

Feature detection and display are the essential goals of the visualization process. Most visualization software achieves these goals by mapping properties of sampled intensity values and their derivatives to color and opacity. In this work, we propose to explicitly study the local frequency distribution of intensity values in broader neighborhoods centered around each voxel. We have found frequency distributions to contain meaningful and quantitative information that is relevant for many kinds of feature queries. Our approach allows users to enter predicate-based hypotheses about relational patterns in local distributions and render visualizations that show how neighborhoods match the predicates. Distributions are a familiar concept to nonexpert users, and we have built a simple graphical user interface for forming and testing queries interactively. The query framework readily applies to arbitrary spatial data sets and supports queries on time variant and multifield data. Users can directly query for classes of features previously inaccessible in general feature detection tools. Using several well-known data sets, we show new quantitative features that enhance our understanding of familiar visualization results.

Reproducible evaluation of spinal cord DTI using an optimized inner volume sequence in combination with probabilistic ROI analysis

The purpose of this work was to reliably acquire and evaluate diffusion tensor data of the cervical spine. Thereto, we describe an optimized, time-efficient inner-volume echo planar imaging sequence. Multislice capability is achieved by restoring the magnetization in neighbouring slices early during the twice refocused diffusion preparation. The acquired diffusion images showed compelling image quality. To reduce the arbitrariness of conventional region of interest (ROI) analysis, a tissue classification algorithm was applied. The classification was independent of the ROI shape and hence, a reliable and stable evaluation of the diffusion tensor could be achieved. The mean fractional anisotropy (FA) of five healthy subjects decreased from C1 (FA = 0.81 +/- 0.03) to C7 (FA = 0.60 +/- 0.03), while the mean apparent diffusion coefficient (ADC) increased from C1 (ADC= 0.78 +/- 0.08 microm2/ms) to C7 (ADC = 1.08 +/- 0.08 microm2/ms). In subsequent measurements of the individual healthy subjects, the standard deviation of the FA was 0.024 +/- 0.011 and the standard deviation of the ADC was 0.045 +/- 0.017 microm2/ms. The FA values of a patient with acute ischemic spinal trauma were significantly lower and changed more drastically than ADC values. Here, absolute FA ranged from 0.23 to 0.42, showing that DTI of the spine may serve as surrogate marker for tissue integrity and therapy monitoring.

Segmentation of MRI brain scans using non-uniform partial volume densities

We present an algorithm that provides a partial volume segmentation of a T1-weighted image of the brain into gray matter, white matter and cerebrospinal fluid. The algorithm incorporates a non-uniform partial volume density that takes the curved nature of the cortex into account. The pure gray and white matter intensities are estimated from the image, using scanner noise and cortical partial volume effects. Expected tissue fractions are subsequently computed in each voxel. The algorithm has been tested for reliability, correct estimation of the pure tissue intensities on both real (repeated) MRI data and on simulated (brain) images. Intra-class correlation coefficients (ICCs) were above 0.93 for all volumes of the three tissue types for repeated scans from the same scanner, as well as for scans with different voxel sizes from different scanners with different field strengths. The implementation of our non-uniform partial volume density provided more reliable volumes and tissue fractions, compared to a uniform partial volume density. Applying the algorithm to simulated images showed that the pure tissue intensities were estimated accurately. Variations in cortical thickness did not influence the accuracy of the volume estimates, which is a valuable property when studying (possible) group differences. In conclusion, we have presented a new partial volume segmentation algorithm that allows for comparisons over scanners and voxel sizes.

MR image segmentation using a power transformation approach

This study proposes a segmentation method for brain MR images using a distribution transformation approach. The method extends traditional Gaussian mixtures expectation-maximization segmentation to a power transformed version of mixed intensity distributions, which includes Gaussian mixtures as a special case. As MR intensities tend to exhibit non-Gaussianity due to partial volume effects, the proposed method is designed to fit non-Gaussian tissue intensity distributions. One advantage of the method is that it is intuitively appealing and computationally simple. To avoid performance degradation caused by intensity inhomogeneity, different methods for correcting bias fields were applied prior to image segmentation, and their correction effects on the segmentation results were examined in the empirical study. The partitions of brain tissues (i.e., gray and white matter) resulting from the method were validated and evaluated against manual segmentation results based on 38 real T1-weighted image volumes from the internet brain segmentation repository, and 18 simulated image volumes from BrainWeb. The Jaccard and Dice similarity indexes were computed to evaluate the performance of the proposed approach relative to the expert segmentations. Empirical results suggested that the proposed segmentation method yielded higher similarity measures for both gray matter and white matter as compared with those based on the traditional segmentation using the Gaussian mixtures approach.

An EM approach to MAP solution of segmenting tissue mixtures: a numerical analysis

This work presents an iterative expectation-maximization (EM) approach to the maximum a posteriori (MAP) solution of segmenting tissue mixtures inside each image voxel. Each tissue type is assumed to follow a normal distribution across the field-of-view (FOV). Furthermore, all tissue types are assumed to be independent from each other. Under these assumptions, the summation of all tissue mixtures inside each voxel leads to the image density mean value at that voxel. The summation of all the tissue mixtures' unobservable random processes leads to the observed image density at that voxel, and the observed image density value also follows a normal distribution (image data are observed to follow a normal distribution in many applications). By modeling the underlying tissue distributions as a Markov random field across the FOV, the conditional expectation of the posteriori distribution of the tissue mixtures inside each voxel is determined, given the observed image data and the current-iteration estimation of the tissue mixtures. Estimation of the tissue mixtures at next iteration is computed by maximizing the conditional expectation. The iterative EM approach to a MAP solution is achieved by a finite number of iterations and reasonable initial estimate. This MAP-EM framework provides a theoretical solution to the partial volume effect, which has been a major cause of quantitative imprecision in medical image processing. Numerical analysis demonstrated its potential to estimate tissue mixtures accurately and efficiently.

Robust MRI brain tissue parameter estimation by multistage outlier rejection

This article addresses the problem of the tissue type parameter estimation in brain MRI in the presence of partial volume effects. Automatic MRI brain tissue classification is hampered by partial volume effects that are caused by the finite resolution of the acquisition process. Due to this effect intensity distributions in brain MRI cannot be well modeled by a simple mixture of Gaussians and therefore more complex models have been developed. Unfortunately, these models do not seem to be robust enough for clinical conditions, as the quality of the tissue classification decreases rapidly with the image quality. Also, the application of these methods for pathological images with unmodeled intensities (e.g. MS plaques, tumors, etc.) remains uncertain. In the present work a new robust method for brain tissue characterization is presented, treating the partial volume affected voxels as outliers of the pure tissue distributions. The proposed method estimates the tissue characteristics from a reduced set of intensities belonging to a particular pure tissue class. This reduced set is selected by using a trimming procedure based on local gradient information and distributional data. This feature makes the method highly tolerant of a large amount of unexpected intensities without degrading its performance. The proposed method has been evaluated using both synthetic and real MR data and compared with state-of-the-art methods showing the best results in the comparative.

SEGMENTATION-FREE MEASURING OF CORTICAL THICKNESS FROM MRI

Estimating the thickness of cerebral cortex is one of the most essential measurements performed in MR brain imaging. In this work we present a new approach to measure the cortical thickness which is based on minimizing line integrals over the probability map of the gray matter in the MRI volume. Previous methods often perform a pre-segmentation of the gray matter before measuring the thickness. Considering the noise and the partial volume effects, there are underlying class probabilities allocated to each voxel that this hard classification ignores, a result of which is a loss of important available information. Following the introduction of the proposed framework, the performance of our method is demonstrated on both artificial volumes and real MRI data for normal and Alzheimer affected subjects.

A modified probabilistic neural network for partial volume segmentation in brain MR image

A modified probabilistic neural network (PNN) for brain tissue segmentation with magnetic resonance imaging (MRI) is proposed. In this approach, covariance matrices are used to replace the singular smoothing factor in the PNN's kernel function, and weighting factors are added in the pattern of summation layer. This weighted probabilistic neural network (WPNN) classifier can account for partial volume effects, which exist commonly in MRI, not only in the final result stage, but also in the modeling process. It adopts the self-organizing map (SOM) neural network to overly segment the input MR image, and yield reference vectors necessary for probabilistic density function (pdf) estimation. A supervised "soft" labeling mechanism based on Bayesian rule is developed, so that weighting factors can be generated along with corresponding SOM reference vectors. Tissue classification results from various algorithms are compared, and the effectiveness and robustness of the proposed approach are demonstrated.

MR brain tissue classification using an edge-preserving spatially variant Bayesian mixture model

In this paper, a spatially constrained mixture model for the segmentation of MR brain images is presented. The novelty of this work is an edge-preserving smoothness prior which is imposed on the probabilities of the voxel labels. This prior incorporates a line process, which is modeled as a Bernoulli random variable, in order to preserve edges between tissues. The main difference with other, state of the art methods imposing priors, is that the constraint is imposed on the probabilities of the voxel labels and not onto the labels themselves. Inference of the proposed Bayesian model is obtained using variational methodology and the model parameters are computed in closed form. Numerical experiments are presented where the proposed model is favorably compared to state of the art brain segmentation methods as well as to a spatially varying Gaussian mixture model.

Classifying CT image data into material fractions by a scale and rotation invariant edge model

A fully automated method is presented to classify 3-D CT data into material fractions. An analytical scale-invariant description relating the data value to derivatives around Gaussian blurred step edges--arch model--is applied to uniquely combine robustness to noise, global signal fluctuations, anisotropic scale, noncubic voxels, and ease of use via a straightforward segmentation of 3-D CT images through material fractions. Projection of noisy data value and derivatives onto the arch yields a robust alternative to the standard computed Gaussian derivatives. This results in a superior precision of the method. The arch-model parameters are derived from a small, but over-determined, set of measurements (data values and derivatives) along a path following the gradient uphill and downhill starting at an edge voxel. The model is first used to identify the expected values of the two pure materials (named L and H) and thereby classify the boundary. Second, the model is used to approximate the underlying noise-free material fractions for each noisy measurement. An iso-surface of constant material fraction accurately delineates the material boundary in the presence of noise and global signal fluctuations. This approach enables straightforward segmentation of 3-D CT images into objects of interest for computer-aided diagnosis and offers an easy tool for the design of otherwise complicated transfer functions in high-quality visualizations. The method is applied to segment a tooth volume for visualization and digital cleansing for virtual colonoscopy.

A computational framework for approximating boundary surfaces in 3-D biomedical images

We propose a new method for detecting and approximating the boundary surfaces in three-dimensional (3-D) biomedical images. Using this method, each boundary surface in the original 3-D image is normalized as a zero-value isosurface of a new 3-D image transformed from the original 3-D image. A novel computational framework is proposed to perform such an image transformation. According to this framework, we first detect boundary surfaces from the original 3-D image and compute discrete samplings of the boundary surfaces. Based on these discrete samplings, a new 3-D image is constructed for each boundary surface such that the boundary surface can be well approximated by a zero-value isosurface in the new 3-D image. In this way, the complex problem of reconstructing boundary surfaces in the original 3-D image is converted into a task to extract a zero-value isosurface from the new 3-D image. The proposed technique is not only capable of adequately reconstructing complex boundary surfaces in 3-D biomedical images, but it also overcomes vital limitations encountered by the isosurface-extracting method when the method is used to reconstruct boundary surfaces from 3-D images. The performances and advantages of the proposed computational framework are illustrated by many examples from different 3-D biomedical images.

Part 1. Automated change detection and characterization in serial MR studies of brain-tumor patients

The goal of this study was to create an algorithm which would quantitatively compare serial magnetic resonance imaging studies of brain-tumor patients. A novel algorithm and a standard classify-subtract algorithm were constructed. The ability of both algorithms to detect and characterize changes was compared using a series of digital phantoms. The novel algorithm achieved a mean sensitivity of 0.87 (compared with 0.59 for classify-subtract) and a mean specificity of 0.98 (compared with 0.92 for classify-subtract) with regard to identification of voxels as changing or unchanging and classification of voxels into types of change. The novel algorithm achieved perfect specificity in seven of the nine experiments. The novel algorithm was additionally applied to a short series of clinical cases, where it was shown to identify visually subtle changes. Automated change detection and characterization could facilitate objective review and understanding of serial magnetic resonance imaging studies in brain-tumor patients.

Assessing disease severity in late infantile neuronal ceroid lipofuscinosis using quantitative MR diffusion-weighted imaging

BACKGROUND AND PURPOSE

Late infantile neuronal ceroid lipofuscinosis (LINCL), a form of Batten disease, is a fatal neurodegenerative genetic disorder, diagnosed via DNA testing, that affects approximately 200 children in the United States at any one time. This study was conducted to evaluate whether quantitative data derived by diffusion-weighted MR imaging (DWI) techniques can supplement clinical disability scale information to provide a quantitative estimate of neurodegeneration, as well as disease progression and severity.

MATERIALS AND METHODS

This study prospectively analyzed 32 DWI examinations from 18 patients having confirmed LINCL at various stages of disease. A whole-brain apparent diffusion coefficient (ADC) histogram was fitted with a dual Gaussian function combined with a function designed to model voxels containing a partial volume fraction of brain parenchyma versus CSF. Previously published whole-brain ADC values of age-matched control subjects were compared with those of the LINCL patients. Correlations were tested between the peak ADC of the fitted histogram and patient age, disease severity, and a CNS disability scale adapted for LINCL.

RESULTS

ADC values assigned to brain parenchyma were higher than published ADC values for age-matched control subjects. ADC values between patients and control subjects began to differ at 5 years of age based on 95% confidence intervals. ADC values had a nearly equal correlation with patient age (R2=0.71) and disease duration (R2=0.68), whereas the correlation with the central nervous system disability scale (R2=0.27) was much weaker.

CONCLUSION

This study indicates that brain ADC values acquired using DWI may be used as an independent measure of disease severity and duration in LINCL.

Volumetric quantification of atherosclerotic plaque in CT considering partial volume effect

Coronary artery calcification (CAC) is quantified based on a computed tomography (CT) scan image. A calcified region is identified. Modified expectation maximization (MEM) of a statistical model for the calcified and background material is used to estimate the partial calcium content of the voxels. The algorithm limits the region over which MEM is performed. By using MEM, the statistical properties of the model are iteratively updated based on the calculated resultant calcium distribution from the previous iteration. The estimated statistical properties are used to generate a map of the partial calcium content in the calcified region. The volume of calcium in the calcified region is determined based on the map. The experimental results on a cardiac phantom, scanned 90 times using 15 different protocols, demonstrate that the proposed method is less sensitive to partial volume effect and noise, with average error of 9.5% (standard deviation (SD) of 5-7mm(3)) compared with 67% (SD of 3-20mm(3)) for conventional techniques. The high reproducibility of the proposed method for 35 patients, scanned twice using the same protocol at a minimum interval of 10 min, shows that the method provides 2-3 times lower interscan variation than conventional techniques.

A study on medical image registration by mutual information with pyramid data structure

The registration method based on mutual information is currently a popular technique for medical image registration, but the computation of the mutual information is complex and the registration speed is slow. In this work, a new slice accumulation pyramid (SAP) data structure was proposed to expedite the registration process. A numerical comparative study between the new data structure and the existing wavelet pyramid (WP) data structure was given, and the results confirmed that the new pyramid data structure was superior to the WP in both the calculation efficiency and the optimizing performance. Finally, SAP was applied to remove the artifacts between CT and MRI data sets, and the results showed the validation of SAP to registration of mulmodality images.