Enhancing the multivariate signal of [15O] water PET studies with a new nonlinear neuroanatomical registration algorithm

Medical image registration: a review

This paper presents a review of automated image registration methodologies that have been used in the medical field. The aim of this paper is to be an introduction to the field, provide knowledge on the work that has been developed and to be a suitable reference for those who are looking for registration methods for a specific application. The registration methodologies under review are classified into intensity or feature based. The main steps of these methodologies, the common geometric transformations, the similarity measures and accuracy assessment techniques are introduced and described.

Deformation invariant attribute vector for deformable registration of longitudinal brain MR images

This paper presents a novel approach to define deformation invariant attribute vector (DIAV) for each voxel in 3D brain image for the purpose of anatomic correspondence detection. The DIAV method is validated by using synthesized deformation in 3D brain MRI images. Both theoretic analysis and experimental studies demonstrate that the proposed DIAV is invariant to general nonlinear deformation. Moreover, our experimental results show that the DIAV is able to capture rich anatomic information around the voxels and exhibit strong discriminative ability. The DIAV has been integrated into a deformable registration algorithm for longitudinal brain MR images, and the results on both simulated and real brain images are provided to demonstrate the good performance of the proposed registration algorithm based on matching of DIAVs.

Effects of image normalization on the statistical analysis of perfusion MRI in elderly brains

PURPOSE

To fully understand the effects of an image processing methodology on the comparisons of regional patterns of brain perfusion over time and between subject groups.

MATERIALS AND METHODS

Two brain normalization methods were compared using images of elderly controls and subjects with MCI and AD: the normalization package of statistical parametric mapping (SPM2), and a fully deformable model (FDM). The performance of these two normalization methods was quantitatively evaluated based on two criteria: (a) the alignment accuracy of five brain structures to the colin27 reference volume, and (b) impact of spatial normalization methods on the sensitivity of perfusion magnetic resonance imaging (pMRI).

RESULTS

The delineations of all five brain structures had significantly higher overlap with expert manual tracings using FDM compared to SPM (two-tailed, P < 0.025). When applied to the biostatistical analysis of CBF maps, a larger number of statistically significant voxels was identified from FDM compared with SPM2 regardless of the effects of the threshold and smoothing kernel.

CONCLUSION

The greater degree of deformation freedom associated with FDM may yield more accurate region matching and higher statistical sensitivity in identifying regions of CBF differences between elderly groups with prevalent late-life neurodegenerative conditions.

Effect of spatial alignment transformations in PCA and ICA of functional neuroimages

It has been previously observed that independent component analysis (ICA), if applied to data pooled in a particular way, may lessen the need for spatial alignment of scans in a functional neuroimaging study. In this paper, we seek to determine analytically the conditions under which this observation is true, not only for spatial ICA, but also for temporal ICA and for principal component analysis (PCA). In each case, we find conditions that the spatial alignment operator must satisfy to ensure invariance of the results. We illustrate our findings using functional magnetic-resonance imaging (fMRI) data. Our analysis is applicable to both intersubject and intrasubject spatial normalization.

Spatial normalization of lesioned brains: performance evaluation and impact on fMRI analyses

A key component of group analyses of neuroimaging data is precise and valid spatial normalization (i.e., inter-subject image registration). When patients have structural brain lesions, such as a stroke, this process can be confounded by the lack of correspondence between the subject and standardized template images. Current procedures for dealing with this problem include regularizing the estimate of warping parameters used to match lesioned brains to the template, or "cost function masking"; both these solutions have significant drawbacks. We report three experiments that identify the best spatial normalization for structurally damaged brains and establish whether differences among normalizations have a significant effect on inferences about functional activations. Our novel protocols evaluate the effects of different normalization solutions and can be applied easily to any neuroimaging study. This has important implications for users of both structural and functional imaging techniques in the study of patients with structural brain damage.

Physically correct mesh manipulation in multi-level free-form deformation-based nonrigid registration

We present a new solution to prevent mesh folding artifacts common in free-form deformation-based nonrigid registration. Our algorithm imposes linear bounds on the search space of control point locations, thereby enabling the use of constrained optimization algorithms. We also introduce a new method for controlling the mesh rigidity, based on maximum voxel displacement. Our method allows local control of the deformation, based on a priori knowledge of the magnitude of possible local deformations.

Retrospective evaluation of a topology preserving non-rigid registration method

This paper proposes a comprehensive evaluation of a monomodal B-spline-based non-rigid registration algorithm allowing topology preservation in 3-D. This article is to be considered as the companion of [Noblet, V., Heinrich, C., Heitz, F., Armspach, J.-P., 2005. 3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization. IEEE Transactions on Image Processing, 14 (5), 553-566] where this algorithm, based on the minimization of an objective function, was introduced and detailed. Overall assessment is based on the estimation of synthetic deformation fields, on average brain construction, on atlas-based segmentation and on landmark mapping. The influence of the model parameters is characterized. Comparison between several objective functions is carried out and impact of their symmetrization is pointed out. An original intensity normalization scheme is also introduced, leading to significant improvements of the registration quality. The comparison benchmark is the popular demons algorithm [Thirion, J.-P., 1998. Image matching as a diffusion process: an analogy with Maxwell's demons. Medical Image Analysis, 2 (3), 243-260], that exhibited best results in a recent comparison between several non-rigid 3-D registration methods [Hellier, P., Barillot, C., Corouge, I., Gibaud, B., Le Goualher, G., Collins, D.L., Evans, A., Malandain, G., Ayache, N., Christensen, G.E., Johnson, H.J., 2003. Retrospective evaluation of intersubject brain registration. IEEE Transactions on Medical Imaging, 22 (9), 1120-1130]. The topology preserving B-spline-based method proved to outperform the commonly available ITK implementation of the demons algorithms on many points. Some limits of intensity-based registration methods are also highlighted through this work.

3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization

This paper deals with topology preservation in three-dimensional (3-D) deformable image registration. This work is a nontrivial extension of, which addresses the case of two-dimensional (2-D) topology preserving mappings. In both cases, the deformation map is modeled as a hierarchical displacement field, decomposed on a multiresolution B-spline basis. Topology preservation is enforced by controlling the Jacobian of the transformation. Finding the optimal displacement parameters amounts to solving a constrained optimization problem: The residual energy between the target image and the deformed source image is minimized under constraints on the Jacobian. Unlike the 2-D case, in which simple linear constraints are derived, the 3-D B-spline-based deformable mapping yields a difficult (until now, unsolved) optimization problem. In this paper, we tackle the problem by resorting to interval analysis optimization techniques. Care is taken to keep the computational burden as low as possible. Results on multipatient 3-D MRI registration illustrate the ability of the method to preserve topology on the continuous image domain.

Quantitative comparison of algorithms for inter-subject registration of 3D volumetric brain MRI scans

The objective of inter-subject registration of three-dimensional volumetric brain scans is to reduce the anatomical variability between the images scanned from different individuals. This is a necessary step in many different applications such as voxelwise group analysis of imaging data obtained from different individuals. In this paper, the ability of three different image registration algorithms in reducing inter-subject anatomical variability is quantitatively compared using a set of common high-resolution volumetric magnetic resonance imaging scans from 17 subjects. The algorithms are from the automatic image registration (AIR; version 5), the statistical parametric mapping (SPM99), and the automatic registration toolbox (ART) packages. The latter includes the implementation of a non-linear image registration algorithm, details of which are presented in this paper. The accuracy of registration is quantified in terms of two independent measures: (1) post-registration spatial dispersion of sets of homologous landmarks manually identified on images before or after registration; and (2) voxelwise image standard deviation maps computed within the set of images registered by each algorithm. Both measures showed that the ART algorithm is clearly superior to both AIR and SPM99 in reducing inter-subject anatomical variability. The spatial dispersion measure was found to be more sensitive when the landmarks were placed after image registration. The standard deviation measure was found sensitive to intensity normalization or the method of image interpolation.

Optimizing the fMRI data-processing pipeline using prediction and reproducibility performance metrics: I. A preliminary group analysis

We argue that published results demonstrate that new insights into human brain function may be obscured by poor and/or limited choices in the data-processing pipeline, and review the work on performance metrics for optimizing pipelines: prediction, reproducibility, and related empirical Receiver Operating Characteristic (ROC) curve metrics. Using the NPAIRS split-half resampling framework for estimating prediction/reproducibility metrics (Strother et al., 2002), we illustrate its use by testing the relative importance of selected pipeline components (interpolation, in-plane spatial smoothing, temporal detrending, and between-subject alignment) in a group analysis of BOLD-fMRI scans from 16 subjects performing a block-design, parametric-static-force task. Large-scale brain networks were detected using a multivariate linear discriminant analysis (canonical variates analysis, CVA) that was tuned to fit the data. We found that tuning the CVA model and spatial smoothing were the most important processing parameters. Temporal detrending was essential to remove low-frequency, reproducing time trends; the number of cosine basis functions for detrending was optimized by assuming that separate epochs of baseline scans have constant, equal means, and this assumption was assessed with prediction metrics. Higher-order polynomial warps compared to affine alignment had only a minor impact on the performance metrics. We found that both prediction and reproducibility metrics were required for optimizing the pipeline and give somewhat different results. Moreover, the parameter settings of components in the pipeline interact so that the current practice of reporting the optimization of components tested in relative isolation is unlikely to lead to fully optimized processing pipelines.

MR-based automatic delineation of volumes of interest in human brain PET images using probability maps

The purpose of this study was to develop and validate an observer-independent approach for automatic generation of volume-of-interest (VOI) brain templates to be used in emission tomography studies of the brain. The method utilizes a VOI probability map created on the basis of a database of several subjects' MR-images, where VOI sets have been defined manually. High-resolution structural MR-images and 5-HT(2A) receptor binding PET-images (in terms of (18)F-altanserin binding) from 10 healthy volunteers and 10 patients with mild cognitive impairment were included for the analysis. A template including 35 VOIs was manually delineated on the subjects' MR images. Through a warping algorithm template VOI sets defined from each individual were transferred to the other subjects MR-images and the voxel overlap was compared to the VOI set specifically drawn for that particular individual. Comparisons were also made for the VOI templates 5-HT(2A) receptor binding values. It was shown that when the generated VOI set is based on more than one template VOI set, delineation of VOIs is better reproduced and shows less variation as compared both to transfer of a single set of template VOIs as well as manual delineation of the VOI set. The approach was also shown to work equally well in individuals with pronounced cerebral atrophy. Probability-map-based automatic delineation of VOIs is a fast, objective, reproducible, and safe way to assess regional brain values from PET or SPECT scans. In addition, the method applies well in elderly subjects, even in the presence of pronounced cerebral atrophy.

Application of a non-linear image registration algorithm to quantitative analysis of T2 relaxation time in transgenic mouse models of AD pathology

Transgenic mouse models have been essential for understanding the pathogenesis of Alzheimer's disease (AD) including those that model the deposition process of beta-amyloid (Abeta). Several laboratories have focused on research related to the non-invasive detection of early changes in brains of transgenic mouse models of Alzheimer's pathology. Most of this work has been performed using regional image analysis of individual mouse brains and pooling the results for statistical assessment. Here we report the implementation of a non-linear image registration algorithm to register anatomical and transverse relaxation time (T2) maps estimated from MR images of transgenic mice. The algorithm successfully registered mouse brain magnetic resonance imaging (MRI) volumes and T2 maps, allowing reliable estimates of T2 values for different regions of interest from the resultant combined images. This approach significantly reduced the data processing and analysis time, and improved the ability to statistically discriminate between groups. Additionally, 3D visualization of intra-regional distributions of T2 of the resultant registered images provided the ability to detect small changes between groups that otherwise would not be possible to detect.

Characterizing changes in MR images with color-coded Jacobians

Image registration is the process of establishing spatial correspondence between two images or between two image volumes. Registration can be achieved by rigid, elastic, or a combination of rigid and elastic transforms that attempt to bring the two images into coincidence. A rigid transform accounts for differences in positioning and an elastic transform describes deformations due to differences in tissue properties, temporal changes due to growth or atrophy, or differences between individuals. Deformation-based morphometry uses the resulting deformation fields from these transforms to evaluate differences between the images being registered. Three methods of registration were evaluated: rigid (affine) transformation, elastic optical flow transformation, and elastic spline transformation. All three methods produce vector deformation fields that map each point in one image to a point in the other image. A 12-color map of the transformation Jacobian was used to represent local volume changes. Using the three registration methods, color-mapped Jacobians were determined using a simulated three-dimensional block with known translation, rotation, expansion, contraction, and intensity modulations. Color-coded Jacobians were also generated for experimentally measured magnetic resonance image volumes of water-filled balloons and 7-year-old twin boys. Color-coded Jacobians overlaid on anatomical images provide a convenient method to identify regional tissue expansion and contraction.

Mutual-information-based registration of medical images: a survey

An overview is presented of the medical image processing literature on mutual-information-based registration. The aim of the survey is threefold: an introduction for those new to the field, an overview for those working in the field, and a reference for those searching for literature on a specific application. Methods are classified according to the different aspects of mutual-information-based registration. The main division is in aspects of the methodology and of the application. The part on methodology describes choices made on facets such as preprocessing of images, gray value interpolation, optimization, adaptations to the mutual information measure, and different types of geometrical transformations. The part on applications is a reference of the literature available on different modalities, on interpatient registration and on different anatomical objects. Comparison studies including mutual information are also considered. The paper starts with a description of entropy and mutual information and it closes with a discussion on past achievements and some future challenges.

The evaluation of preprocessing choices in single-subject BOLD fMRI using NPAIRS performance metrics

This work proposes an alternative to simulation-based receiver operating characteristic (ROC) analysis for assessment of fMRI data analysis methodologies. Specifically, we apply the rapidly developing nonparametric prediction, activation, influence, and reproducibility resampling (NPAIRS) framework to obtain cross-validation-based model performance estimates of prediction accuracy and global reproducibility for various degrees of model complexity. We rely on the concept of an analysis chain meta-model in which all parameters of the preprocessing steps along with the final statistical model are treated as estimated model parameters. Our ROC analog, then, consists of plotting prediction vs. reproducibility results as curves of model complexity for competing meta-models. Two theoretical underpinnings are crucial to utilizing this new validation technique. First, we explore the relationship between global signal-to-noise and our reproducibility estimates as derived previously. Second, we submit our model complexity curves in the prediction versus reproducibility space as reflecting classic bias-variance tradeoffs. Among the particular analysis chains considered, we found little impact in performance metrics with alignment, some benefit with temporal detrending, and greatest improvement with spatial smoothing.

Fast parametric elastic image registration

We present an algorithm for fast elastic multidimensional intensity-based image registration with a parametric model of the deformation. It is fully automatic in its default mode of operation. In the case of hard real-world problems, it is capable of accepting expert hints in the form of soft landmark constraints. Much fewer landmarks are needed and the results are far superior compared to pure landmark registration. Particular attention has been paid to the factors influencing the speed of this algorithm. The B-spline deformation model is shown to be computationally more efficient than other alternatives. The algorithm has been successfully used for several two-dimensional (2-D) and three-dimensional (3-D) registration tasks in the medical domain, involving MRI, SPECT, CT, and ultrasound image modalities. We also present experiments in a controlled environment, permitting an exact evaluation of the registration accuracy. Test deformations are generated automatically using a random hierarchical fractional wavelet-based generator.

The quantitative evaluation of functional neuroimaging experiments: mutual information learning curves

Learning curves are presented as an unbiased means for evaluating the performance of models for neuroimaging data analysis. The learning curve measures the predictive performance in terms of the generalization or prediction error as a function of the number of independent examples (e.g., subjects) used to determine the parameters in the model. Cross-validation resampling is used to obtain unbiased estimates of a generic multivariate Gaussian classifier, for training set sizes from 2 to 16 subjects. We apply the framework to four different activation experiments, in this case [(15)O]water data sets, although the framework is equally valid for multisubject fMRI studies. We demonstrate how the prediction error can be expressed as the mutual information between the scan and the scan label, measured in units of bits. The mutual information learning curve can be used to evaluate the impact of different methodological choices, e.g., classification label schemes, preprocessing choices. Another application for the learning curve is to examine the model performance using bias/variance considerations enabling the researcher to determine if the model performance is limited by statistical bias or variance. We furthermore present the sensitivity map as a general method for extracting activation maps from statistical models within the probabilistic framework and illustrate relationships between mutual information and pattern reproducibility as derived in the NPAIRS framework described in a companion paper.

Quantitative comparison and analysis of brain image registration using frequency-adaptive wavelet shrinkage

In the field of template-based medical image analysis, image registration and normalization are frequently used to evaluate and interpret data in a standard template or reference atlas space. Despite the large number of image-registration (warping) techniques developed recently in the literature, only a few studies have been undertaken to numerically characterize and compare various alignment methods. In this paper, we introduce a new approach for analyzing image registration based on a selective-wavelet reconstruction technique using a frequency-adaptive wavelet shrinkage. We study four polynomial-based and two higher complexity nonaffine warping methods applied to groups of stereotaxic human brain structural (magnetic resonance imaging) and functional (positron emission tomography) data. Depending upon the aim of the image registration, we present several warp classification schemes. Our method uses a concise representation of the native and resliced (pre- and post-warp) data in compressed wavelet space to assess quality of registration. This technique is computationally inexpensive and utilizes the image compression, image enhancement, and denoising characteristics of the wavelet-based function representation, as well as the optimality properties of frequency-dependent wavelet shrinkage.

Deformation-Based Morphometry and Its Relation to Conventional Volumetry of Brain Lateral Ventricles in MRI

Deformation-based morphometry (DBM) is a useful technique to detect morphological differences over the entire brain since it analyses positional differences between every voxel and a standard brain. In this report we compare DBM to semimanual tracing of brain ventricles in a population of 39 patients with schizophrenia. High-resolution T(1)-weighted magnetic resonance images were obtained and processed with DBM and interactive tracing software. We evaluate the validity of the DBM in two different approaches. First, we divide subjects into two groups based on the mean ventricular/brain ratios and compute statistical maps of displacement vectors and their spatial derivatives. This analysis demonstrates a striking consistency of the DBM and visual tracing results. We show that restricting the information about the deformation fields by computing the local Jacobian determinant (as a measure of volume change) provides evidence of the shape of ventricular deformation which is unavailable from ventricular volume measures alone. Second, we compute a mean measure of the Jacobian values over the entire ventricles and observe a correlation of r = 0.962 with visual tracing based ventricular/brain ratios. The results support the usefulness and validity of DBM for the local and global examination of brain morphology.

Penalized discriminant analysis of [15O]-water PET brain images with prediction error selection of smoothness and regularization hyperparameters

We propose a flexible, comprehensive approach for analysis of [15O]-water positron emission tomography (PET) brain images using a penalized version of linear discriminant analysis (PDA). We applied it to scans from 20 subjects (eight scans/subject) performing a finger movement task and analyzed: 1) two classes to obtain a covariance-normalized baseline-activation image, and 2) eight classes for the mean within subject temporal structure which contained baseline-activation and time-dependent changes in a two-dimensional canonical subspace. We imposed spatial smoothness on the resulting image(s) by expanding it in five tensor-product B-spline (TPS) bases of varying smoothness, and further regularized with a ridge-type penalty on the noise covariance matrix. The discrimination approach of PDA provides a probabilistic framework within which prediction error (PE) estimates are derived. We used these to optimize over TPS bases and a ridge hyperparameter (expressed as equivalent degrees of freedom, EDF). We obtained unbiased, low variance PE estimates using modern resampling tools (.632+ Bootstrap and cross validation), and compared PDA of 1) TPS-projected, mean-normalized and unnormalized scans and 2) mean-normalized scans with and without additional presmoothing. By examining the tradeoffs between PE and EDF, as a function of basis selection and image smoothing we demonstrate the utility of PDA, the PE framework, and the relationship between singular value decomposition and smooth TPS bases in the analysis of functional neuroimages.

Accuracy and sensitivity of detection of activation foci in the brain via statistical parametric mapping: a study using a PET simulator

Statistical parametric mapping (SPM) is currently the most widely used method for analysis of functional activation images. This paper reports a quantitative evaluation of the sensitivity and accuracy of SPM, using a realistic simulator of PET image formation, which accounted for the main physical processes involved in PET, including attenuation, scatter, randoms, Poisson noise, and limited detector resolution. Activation foci of the brain were simulated by placing spheres of specified activities in particular locations. Using these data, the sensitivity and accuracy of SPM in detecting activation foci was measured for different versions of the SPM spatial normalization method and for an elastic warping method referred to as STAR (spatial transformation algorithm for registration). The STAR method resulted in relatively better registration and hence better detection of the activation foci. A secondary goal of the paper was to evaluate the improvement in detection sensitivity obtained by applying an atlas-based adaptive smoothing method instead of the usual Gaussian filtering method. The results indicate some limitations of statistical parametric mapping, assist in the correct interpretation of the SPM maps, and point to future research directions in functional image analysis.

The role of image registration in brain mapping

Image registration is a key step in a great variety of biomedical imaging applications. It provides the ability to geometrically align one dataset with another, and is a prerequisite for all imaging applications that compare datasets across subjects, imaging modalities, or across time. Registration algorithms also enable the pooling and comparison of experimental findings across laboratories, the construction of population-based brain atlases, and the creation of systems to detect group patterns in structural and functional imaging data. We review the major types of registration approaches used in brain imaging today. We focus on their conceptual basis, the underlying mathematics, and their strengths and weaknesses in different contexts. We describe the major goals of registration, including data fusion, quantification of change, automated image segmentation and labeling, shape measurement, and pathology detection. We indicate that registration algorithms have great potential when used in conjunction with a digital brain atlas, which acts as a reference system in which brain images can be compared for statistical analysis. The resulting armory of registration approaches is fundamental to medical image analysis, and in a brain mapping context provides a means to elucidate clinical, demographic, or functional trends in the anatomy or physiology of the brain.

Comparison of matched BOLD and FAIR 4.0T-fMRI with [15O]water PET brain volumes

Valid comparisons of functional activation volumes from fMRI and PET require accurate registration, matched spatial resolution, and if possible matched noise. We coregistered 4.0T-fMRI and PET volumes, using a series of linear and nonlinear transformations applied to the PET volumes. Because of the limited number of fMRI slices that were available, PET volumes were transformed to the fMRI space. Since 4.0T-fMRI and 4.0T-MRI volumes have significant spatial distortion due to magnet inhomogeneities, high resolution 1.5T-MRI volumes were nonlinearly transformed to 4.0T-MRI volumes as part of the transformation chain. The smoothing effects of these registration transformations were measured, in order to match the spatial resolution of the coregistered fMRI and PET volumes. Spatial resolution of the transformed PET volumes in the fMRI space was degraded by up to 60% due to the transformation process. Due to both the image acquisition characteristics and the coregistration process, the transformed PET volumes had a spatial resolution that was lower than that of tMRI. Therefore, significant smoothing of fMRI volumes was necessary to match their spatial resolution with that of the transformed PET volumes. Matching the spatial resolution of the fMRI volumes to those of the transformed PET volumes was achieved by matching the shape of their point spread functions. In order to do this, Gaussian kernels were employed to smooth the fMRI volumes. We were unable to simultaneously match the resolution and noise of fMRI and PET signals in the motor cortex. Activation maps derived from transformed PET and smoothed fMRI volumes were compared. Contralateral motor cortex was active in all modalities but there were large variations in the size of the activated region and its signal to noise ratio across BOLD, FAIR, and PET images within each subject. Nevertheless, the relative CBF changes measured by FAIR were consistent with those determined by PET.