Diffeomorphic Registration Algorithm Research Articles

A Novel 3D-to-3D Diffeomorphic Registration Algorithm With Applications to Left Ventricle Segmentation in MR and Ultrasound Sequences

Left ventricular segmentation is a difficult and time-consuming task performed by clinicians, requiring the use of manual contours. We propose a novel three-dimensional diffeomorphic registration algorithm for endocardial segmentation of the left ventricle in magnetic resonance images and ultrasound temporal sequences. The proposed diffeomorphic registration method computes a voxel-to-voxel correspondence in three-dimensional space and is parameterized by one radial and three curl components to emulate the cardiac deformations. In addition, the proposed method allows for enforcing constraints to control the amount of deformation. The method was evaluated on 521 temporal frames from 20 patients from the Automated Cardiac Diagnosis Challenge magnetic resonance imaging dataset and 213 frames from 10 patients undergoing ultrasound scans from the Mazankowski Alberta Heart Institute. The algorithm was compared against six other registration methods, the Symmetric Normalization algorithm from the Dipy package, two variants of the Demons algorithm from the Insight Toolkit software package, two versions of RealTiTracker, and Elastix. The proposed method yielded overall Dice scores of 98.10 (0.90)% for the MRI dataset and 92.90 (2.42)% for the ultrasound dataset. The robustness of the algorithm is demonstrated by the high performance on multiple imaging modalities and various patient abnormalities.

Optimizing MRI Registration using Software/Hardware Co-Design Model on FPGA

The correct localization of brain tissue deformation and determination of the tumor growth relies majorly on the accuracy of the process known by image registration. Poor registration may lead to misclassified diseases and highly affect image-guided surgery and radiation therapies. Voxel-based morphometry (VBM) is an image analytical technique encompassing accurate registration but suffers from intensive time computations, similar to most of image registration techniques. Achieving the compromise between accuracy and computations is a challenging mission. Field programmable gate arrays have fast-evolving and customizable hardware acceleration capabilities that promise to help speed up computational tasks. This paper presents a software/hardware co-design model for accelerating the implementation of the diffeomorphic image registration algorithm ‘DARTEL’ as a part of VBM that analyzes MRI images. An optimized and pipelined hardware architecture is proposed and integrated into the Statistical Parametric Mapping (SPM) software tool that runs the DARTEL. Acceleration of the DARTEL registration algorithm resulted in a speedup factor of 114x on function-level, compared to the CPU with a contribution of 8x faster for the overall performance in the registration process of the SPM. The proposed model is successfully validated for the identification of Alzheimer’s disease based on T1-weighted MRI. A proposed software/hardware co-design model for VBM achieves remarkable acceleration while maintaining classification accuracy and proving proficiency against other CPU and GPU implementations.

Validation of Diffeomorphic Registration on Cine Cardiac MR via Direct Frame-to-Frame Comparison with HARP Tracking on Tagged MR.

Cardiac magnetic resonance (MR) tissue tagging offers an excellent solution for tracking deformation and is considered the reference standard for the quantification of strain. However, due to the requirements for a dedicated acquisition sequence and post-processing software, tagged MR acquisitions are performed much less frequently in routine clinical practice than the anatomical cine MR sequence. Using tagged MR as the reference standard, this study proposes an approach to evaluate a diffeomorphic image registration algorithm applied on cine MR images to compute the cardiac deformation. In contrast to previous evaluation methods that compared the final results, such as strain, computed from cine and tagged MR sequences, the proposed method performs a direct frame-to-frame comparison in the evaluation. To overcome the problem of misalignment between the tagged and cine MR images, the proposed approach performs transformations to and from the two-dimensional image pixel coordinates and three-dimensional space using the meta-information encoded in the MR images. Linear temporal interpolation is performed using the frame acquisition time since the last R-wave peak value of the electrocardiogram signal recorded in the meta-information. Several statistic measures are computed and reported for the registration error using the Euclidean distances between the corresponding set of points obtained using cine and tagged MR images.

Validation of a diffeomorphic registration algorithm using true deformation computed from thin plate spline interpolation.

Despite the inter and intraobserver variabilities, manual contours are commonly used as surrogates for ground truth in the validation process for nonrigid medical image registration. In contrast, this study proposes the use of thin plate spline interpolation to create a true deformation field. A diffeomorphic registration method was compared to the true deformation field along with three other algorithms and was evaluated on simulated cardiac motion deformation over 10 subjects from the Automated Cardiac Diagnosis Challenge (ACDC) dataset. Two sequential registration approaches were undertaken: with respect to the first frame, and with respect to the previous frame. The Dice score was calculated between the simulated and warped contours for the two approaches: diffeomorphic registration method =0.991 and 0.997, RealTITracker (L2L2 method) = 0.971 and 0.977, RealTITracker (L2L1 method) = 0.975 and 0.978, and Elastix = 0.976 and 0.994. The results demonstrate the robust performance of the diffeomorphic registration method.Clinical relevance This establishes a validation of a registration method that can be used for segmentation of chambers of the heart.

Right ventricular shape and function: cardiovascular magnetic resonance reference morphology and biventricular risk factor morphometrics in UK Biobank

BackgroundThe associations between cardiovascular disease (CVD) risk factors and the biventricular geometry of the right ventricle (RV) and left ventricle (LV) have been difficult to assess, due to subtle and complex shape changes. We sought to quantify reference RV morphology as well as biventricular variations associated with common cardiovascular risk factors.MethodsA biventricular shape atlas was automatically constructed using contours and landmarks from 4329 UK Biobank cardiovascular magnetic resonance (CMR) studies. A subdivision surface geometric mesh was customized to the contours using a diffeomorphic registration algorithm, with automatic correction of slice shifts due to differences in breath-hold position. A reference sub-cohort was identified consisting of 630 participants with no CVD risk factors. Morphometric scores were computed using linear regression to quantify shape variations associated with four risk factors (high cholesterol, high blood pressure, obesity and smoking) and three disease factors (diabetes, previous myocardial infarction and angina).ResultsThe atlas construction led to an accurate representation of 3D shapes at end-diastole and end-systole, with acceptable fitting errors between surfaces and contours (average error less than 1.5 mm). Atlas shape features had stronger associations than traditional mass and volume measures for all factors (p < 0.005 for each). High blood pressure was associated with outward displacement of the LV free walls, but inward displacement of the RV free wall and thickening of the septum. Smoking was associated with a rounder RV with inward displacement of the RV free wall and increased relative wall thickness.ConclusionMorphometric relationships between biventricular shape and cardiovascular risk factors in a large cohort show complex interactions between RV and LV morphology. These can be quantified by z-scores, which can be used to study the morphological correlates of disease.

An Iterative Diffeomorphic Algorithm for Registration of Subdivision Surfaces: Application to Congenital Heart Disease.

In this paper, we present a new diffeomorphic registration algorithm for the registration of 3D models to 3D points. A biventricular template is iteratively fitted to the data by a series of implicitly constrained diffeomorphic linear least squares fits with decreasing regularization weights before performing an explicitly constrained diffeomorphic fit. The algorithm has been tested on a set of manual contours from 20 patients with a variety of congenital heart disease. Registration accuracy was assessed by calculating the mean point-to-point distance and the Dice overlap metric. Results showed that the method was able to accurately fit the biventricular model to 3D points and that the deformable model was able to fit all the pathologies while being diffeomorphic. The algorithm took approximately 5 minutes to fit each case, with an average of 52,580 points per case.

Longitudinal Analysis of Image Time Series with Diffeomorphic Deformations: A Computational Framework Based on Stationary Velocity Fields.

We propose and detail a deformation-based morphometry computational framework, called Longitudinal Log-Demons Framework (LLDF), to estimate the longitudinal brain deformations from image data series, transport them in a common space and perform statistical group-wise analyses. It is based on freely available software and tools, and consists of three main steps: (i) Pre-processing, (ii) Position correction, and (iii) Non-linear deformation analysis. It is based on the LCC log-Demons non-linear symmetric diffeomorphic registration algorithm with an additional modulation of the similarity term using a confidence mask to increase the robustness with respect to brain boundary intensity artifacts. The pipeline is exemplified on the longitudinal Open Access Series of Imaging Studies (OASIS) database and all the parameters values are given so that the study can be reproduced. We investigate the group-wise differences between the patients with Alzheimer's disease and the healthy control group, and show that the proposed pipeline increases the sensitivity with no decrease in the specificity of the statistical study done on the longitudinal deformations.

Diffeomorphic registration with self-adaptive spatial regularization for the segmentation of non-human primate brains.

Cerebral aging has been linked to structural and functional changes in the brain throughout life. Here, we study the marmoset, a small non-human primate, in order to get insights into the mechanisms of brain aging in normal and pathological conditions. Imaging the brain of small animals with techniques such as MRI, quickly becomes a challenging task when compared with human brain imaging. Very often, a simple pre-processing step such as brain extraction cannot be achieved with classical tools. In this paper, we propose a diffeomorphic registration algorithm, which makes use of learned constraints to propagate the manual segmentation of a marmoset brain template to other MR images of marmoset brains. The main methological contribution of our paper is to explore a new strategy to automatically tune the spatial regularization of the deformations. Results show that we obtain a robust segmentation of the brain, even for images with a low contrast.

Validation of an Improved ‘Diffeomorphic Demons’ Algorithm for Deformable Image Registration in Image-Guided Radiation Therapy

Deformable image registration (DIR) was widely used in radiation therapy, such as in automatic contour generation, dose accumulation, tumor growth or regression analysis. To achieve higher registration accuracy and faster convergence, an improved 'diffeomorphic demons' registration algorithm was proposed and validated. Based on Brox et al.'s gradient constancy assumption and Malis's efficient second-order minimization (ESM) algorithm, a grey value gradient similarity term and a transformation error term were added into the demons energy function, and a formula was derived to calculate the update of transformation field. The limited Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm was used to optimize the energy function so that the iteration number could be determined automatically. The proposed algorithm was validated using mathematically deformed images and physically deformed phantom images. Compared with the original 'diffeomorphic demons' algorithm, the registration method proposed achieve a higher precision and a faster convergence speed. Due to the influence of different scanning conditions in fractionated radiation, the density range of the treatment image and the planning image may be different. In such a case, the improved demons algorithm can achieve faster and more accurate radiotherapy.

LCC-Demons: A robust and accurate symmetric diffeomorphic registration algorithm

Non-linear registration is a key instrument for computational anatomy to study the morphology of organs and tissues. However, in order to be an effective instrument for the clinical practice, registration algorithms must be computationally efficient, accurate and most importantly robust to the multiple biases affecting medical images. In this work we propose a fast and robust registration framework based on the log-Demons diffeomorphic registration algorithm. The transformation is parameterized by stationary velocity fields (SVFs), and the similarity metric implements a symmetric local correlation coefficient (LCC). Moreover, we show how the SVF setting provides a stable and consistent numerical scheme for the computation of the Jacobian determinant and the flux of the deformation across the boundaries of a given region. Thus, it provides a robust evaluation of spatial changes. We tested the LCC-Demons in the inter-subject registration setting, by comparing with state-of-the-art registration algorithms on public available datasets, and in the intra-subject longitudinal registration problem, for the statistically powered measurements of the longitudinal atrophy in Alzheimer's disease. Experimental results show that LCC-Demons is a generic, flexible, efficient and robust algorithm for the accurate non-linear registration of images, which can find several applications in the field of medical imaging. Without any additional optimization, it solves equally well intra & inter-subject registration problems, and compares favorably to state-of-the-art methods.

A Sharp Sufficient Condition for B-Spline Vector Field Invertibility. Application to Diffeomorphic Registration and Interslice Interpolation

In this paper, a new sufficient condition for the invertibility of a B-spline vector field as well as its extension to spatio-temporal vector fields are presented. The new condition, while guaranteeing that the vector field is diffeomorphic, is sharp enough to allow large deformations. The complexity of the constraint is also discussed. A new diffeomorphic registration algorithm using this condition and its application to interslice interpolation are presented and evaluated on synthetic images and in vivo magnetic resonance $T_2$ images of the brain. The registration method has also been compared to some state-of-the-art registration methods.

Ontological labels for automated location of anatomical shape differences

A method for automated location of shape differences in diseased anatomical structures via high resolution biomedical atlases annotated with labels from formal ontologies is described. In particular, a high resolution magnetic resonance image of the myocardium of the human left ventricle was segmented and annotated with structural terms from an extracted subset of the Foundational Model of Anatomy ontology. The atlas was registered to the end systole template of a previous study of left ventricular remodeling in cardiomyopathy using a diffeomorphic registration algorithm. The previous study used thresholding and visual inspection to locate a region of statistical significance which distinguished patients with ischemic cardiomyopathy from those with nonischemic cardiomyopathy. Using semantic technologies and the deformed annotated atlas, this location was more precisely found. Although this study used only a cardiac atlas, it provides a proof-of-concept that ontologically labeled biomedical atlases of any anatomical structure can be used to automate location-based inferences.

Increased gray matter density in patients with schizophrenia and cannabis use: A voxel-based morphometric study using DARTEL

Alterations in gray matter density as well as cognitive impairments are commonly described in patients with schizophrenia (SCH patients). Both gray matter deficits and cognitive impairments have recently been discussed to represent vulnerability markers of schizophrenia. The counterintuitive finding of better cognitive performance in patients with schizophrenia and cannabis use (SCH+CAN patients) compared to cannabis naïve patients is discussed as a reflection of lower vulnerability for schizophrenia in at least one subgroup of SCH+CAN patients. We hypothesized that SCH+CAN patients would display fewer gray matter deficits compared to SCH patients reflecting their presumed lower vulnerability. We therefore compared gray matter density in 30 first episode SCH+CAN and 24 first episode SCH patients using a fast diffeomorphic registration algorithm (DARTEL) and voxel-based morphometry (VBM). We found less severe cognitive impairments and middle frontal gray matter deficits in the SCH+CAN patients. In the pooled sample gray matter density was positively associated with cognitive functioning. Results may support the hypothesis of a lower biological vulnerability in at least one subgroup of SCH+CAN patients.

Diffeomorphic Metric Mapping of High Angular Resolution Diffusion Imaging Based on Riemannian Structure of Orientation Distribution Functions

In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. To this end, we first review the Riemannian manifold of ODFs. We then define the reorientation of an ODF when an affine transformation is applied and subsequently, define the diffeomorphic group action to be applied on the ODF based on this reorientation. We incorporate the Riemannian metric of ODFs for quantifying the similarity of two HARDI images into a variational problem defined under the large deformation diffeomorphic metric mapping framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.

Left Anterior Temporal Lobe Sustains Naming in Alzheimers Dementia and Mild Cognitive Impairment

Cognitive decline in degenerative dementia is paralleled by progressive brain atrophy, with the localization of atrophy reflecting specific cognitive impairment. Confrontation naming deficits are frequently observed in dementia across etiologies. In this study we aimed to identify the brain regions underlying this deficit. In patients with clinically diagnosed dementia or mild cognitive impairment (MCI) we investigated the relationship between gray matter volume (GMV) and performance on a standardized confrontation naming test. 268 patients with one of three probable etiologies were included: Alzheimer's Dementia (AD), AD with signs of cerebrovascular pathology, and frontotemporal dementia. Applying voxel-based morphometry using a diffeomorphic registration algorithm we contrasted GMV of patients performing within the normal range with those of patients with pathological performance. Further, differential effects of gray matter atrophy on impaired performance in AD versus MCI of AD type were investigated. Results revealed significantly reduced GMV in the left anterior temporal lobe (ATL) in pathological performers compared to normal performers. The subgroup analysis confined to MCI of AD type and AD patients confirmed this relationship. While left ATL atrophy is known to be implicated in naming deficits in semantic dementia, our data confirm the same in AD and MCI of AD type.

Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation

In the context of large deformations by diffeomorphisms, we propose a new diffeomorphic registration algorithm for 3D images that performs the optimization directly on the set of geodesic flows. The key contribution of this work is to provide an accurate estimation of the so-called initial momentum, which is a scalar function encoding the optimal deformation between two images through the Hamiltonian equations of geodesics. Since the initial momentum has proven to be a key tool for statistics on shape spaces, our algorithm enables more reliable statistical comparisons for 3D images. Our proposed algorithm is a gradient descent on the initial momentum, where the gradient is calculated using standard methods from optimal control theory. To improve the numerical efficiency of the gradient computation, we have developed an integral formulation of the adjoint equations associated with the geodesic equations. We then apply it successfully to the registration of 2D phantom images and 3D cerebral images. By comparing our algorithm to the standard approach of Beg et al. (Int. J. Comput. Vis. 61:139---157, 2005), we show that it provides a more reliable estimation of the initial momentum for the optimal path. In addition to promising statistical applications, we finally discuss different perspectives opened by this work, in particular in the new field of longitudinal analysis of biomedical images.

Diffeomorphic demons: Efficient non-parametric image registration

We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. In the first part of this paper, we show that Thirion's demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion's demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of displacement fields by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians.