Brad Davis

Unbiased diffeomorphic atlas construction for computational anatomy

Construction of population atlases is a key issue in medical image analysis, and particularly in brain mapping. Large sets of images are mapped into a common coordinate system to study intra-population variability and inter-population differences, to provide voxel-wise mapping of functional sites, and help tissue and object segmentation via registration of anatomical labels. Common techniques often include the choice of a template image, which inherently introduces a bias. This paper describes a new method for unbiased construction of atlases in the large deformation diffeomorphic setting. A child neuroimaging autism study serves as a driving application. There is lack of normative data that explains average brain shape and variability at this early stage of development. We present work in progress toward constructing an unbiased MRI atlas of 2 years of children and the building of a probabilistic atlas of anatomical structures, here the caudate nucleus. Further, we demonstrate the segmentation of new subjects via atlas mapping. Validation of the methodology is performed by comparing the deformed probabilistic atlas with existing manual segmentations.

Large deformation three-dimensional image registration in image-guided radiation therapy

In this paper, we present and validate a framework, based on deformable image registration, for automatic processing of serial three-dimensional CT images used in image-guided radiation therapy. A major assumption in deformable image registration has been that, if two images are being registered, every point of one image corresponds appropriately to some point in the other. For intra-treatment images of the prostate, however, this assumption is violated by the variable presence of bowel gas. The framework presented here explicitly extends previous deformable image registration algorithms to accommodate such regions in the image for which no correspondence exists. We show how to use our registration technique as a tool for organ segmentation, and present a statistical analysis of this segmentation method, validating it by comparison with multiple human raters. We also show how the deformable registration technique can be used to determine the dosimetric effect of a given plan in the presence of non-rigid tissue motion. In addition to dose accumulation, we describe a method for estimating the biological effects of tissue motion using a linear-quadratic model. This work is described in the context of a prostate treatment protocol, but it is of general applicability.

Population Shape Regression From Random Design Data

Regression analysis is a powerful tool for the study of changes in a dependent variable as a function of an independent regressor variable, and in particular it is applicable to the study of anatomical growth and shape change. When the underlying process can be modeled by parameters in a Euclidean space, classical regression techniques are applicable and have been studied extensively. However, recent work suggests that attempts to describe anatomical shapes using flat Euclidean spaces undermines our ability to represent natural biological variability. In this paper we develop a method for regression analysis of general, manifold-valued data. Specifically, we extend Nadaraya-Watson kernel regression by recasting the regression problem in terms of Frechet expectation. Although this method is quite general, our driving problem is the study anatomical shape change as a function of age from random design image data. We demonstrate our method by analyzing shape change in the brain from a random design dataset of MR images of 89 healthy adults ranging in age from 22 to 79 years. To study the small scale changes in anatomy, we use the infinite dimensional manifold of diffeomorphic transformations, with an associated metric. We regress a representative anatomical shape, as a function of age, from this population.

Multi-Modal Image Set Registration and Atlas Formation

In this paper, we present a Bayesian framework for both generating inter-subject large deformation transformations between two multi-modal image sets of the brain and for forming multi-class brain atlases. In this framework, the estimated transformations are generated using maximal information about the underlying neuroanatomy present in each of the different modalities. This modality independent registration framework is achieved by jointly estimating the posterior probabilities associated with the multi-modal image sets and the high-dimensional registration transformations mapping these posteriors. To maximally use the information present in all the modalities for registration, Kullback-Leibler divergence between the estimated posteriors is minimized. Registration results for image sets composed of multi-modal MR images of healthy adult human brains are presented. Atlas formation results are presented for a population of five infant human brains.

Evaluation of an automated deformable image matching method for quantifying lung motion in respiration‐correlated CT images

We have evaluated an automated registration procedure for predicting tumor and lung deformation based on CT images of the thorax obtained at different respiration phases. The method uses a viscous fluid model of tissue deformation to map voxels from one CT dataset to another. To validate the deformable matching algorithm we used a respiration-correlated CT protocol to acquire images at different phases of the respiratory cycle for six patients with nonsmall cell lung carcinoma. The position and shape of the deformable gross tumor volumes (GTV) at the end-inhale (EI) phase predicted by the algorithm was compared to those drawn by four observers. To minimize interobserver differences, all observers used the contours drawn by a single observer at end-exhale (EE) phase as a guideline to outline GTV contours at EI. The differences between model-predicted and observer-drawn GTV surfaces at EI, as well as differences between structures delineated by observers at EI (interobserver variations) were evaluated using a contour comparison algorithm written for this purpose, which determined the distance between the two surfaces along different directions. The mean and 90% confidence interval for model-predicted versus observer-drawn GTV surface differences over all patients and all directions were 2.6 and 5.1 mm, respectively, whereas the mean and 90% confidence interval for interobserver differences were 2.1 and 3.7 mm. We have also evaluated the algorithms ability to predict normal tissue deformations by examining the three-dimensional (3-D) vector displacement of 41 landmarks placed by each observer at bronchial and vascular branch points in the lung between the EE and EI image sets (mean and 90% confidence interval displacements of 11.7 and 25.1 mm, respectively). The mean and 90% confidence interval discrepancy between model-predicted and observer-determined landmark displacements over all patients were 2.9 and 7.3 mm, whereas interobserver discrepancies were 2.8 and 6.0 mm. Paired t tests indicate no significant statistical differences between model predicted and observer drawn structures. We conclude that the accuracy of the algorithm to map lung anatomy in CT images at different respiratory phases is comparable to the variability in manual delineation. This method has therefore the potential for predicting and quantifying respiration-induced tumor motion in the lung.

Unbiased atlas formation via large deformations metric mapping

The construction of population atlases is a key issue in medical image analysis, and particularly in brain mapping. Large sets of images are mapped into a common coordinate system to study intra-population variability and inter-population differences, to provide voxel-wise mapping of functional sites, and to facilitate tissue and object segmentation via registration of anatomical labels. We formulate the unbiased atlas construction problem as a Fréchet mean estimation in the space of diffeomorphisms via large deformations metric mapping. A novel method for computing constant speed velocity fields and an analysis of atlas stability and robustness using entropy are presented. We address the question: how many images are required to build a stable brain atlas?

Automatic segmentation of intra-treatment CT images for adaptive radiation therapy of the prostate

We have been developing an approach for automatically quantifying organ motion for adaptive radiation therapy of the prostate. Our approach is based on deformable image registration, which makes it possible to establish a correspondence between points in images taken on different days. This correspondence can be used to study organ motion and to accumulate inter-fraction dose. In prostate images, however, the presence of bowel gas can cause significant correspondence errors. To account for this problem, we have developed a novel method that combines large deformation image registration with a bowel gas segmentation and deflation algorithm. In this paper, we describe our approach and present a study of its accuracy for adaptive radiation therapy of the prostate. All experiments are carried out on 3-dimensional CT images.

Large deformation minimum mean squared error template estimation for computational anatomy

This paper presents a method for large deformation exemplar template estimation. This method generates a representative anatomical template from an arbitrary number of topologically similar images using large deformation minimum mean squared error image registration. The template that we generate is the image that requires the least amount of deformation energy to be transformed into every input image. We show that this method is also useful for image registration. In particular, it provides a means for inverse consistent image registration. This method is computationally practical; computation time grows linearly with the number of input images. Template estimation results are presented for a set of five 3D MR human brain images.

Improved correspondence for DTI population studies via unbiased atlas building

We present a method for automatically finding correspondence in Diffusion Tensor Imaging (DTI) from deformable registration to a common atlas. The registration jointly produces an average DTI atlas, which is unbiased with respect to the choice of a template image, along with diffeomorphic correspondence between each image. The registration image match metric uses a feature detector for thin fiber structures of white matter, and interpolation and averaging of diffusion tensors use the Riemannian symmetric space framework. The anatomically significant correspondence provides a basis for comparison of tensor features and fiber tract geometry in clinical studies and for building DTI population atlases.

Multi-class Posterior Atlas Formation via Unbiased Kullback-Leibler Template Estimation

Many medical image analysis problems that involve multi-modal images lend themselves to solutions that involve class posterior density function images. This paper presents a method for large deformation exemplar class posterior density template estimation. This method generates a representative anatomical template from an arbitrary number of topologically similar multi-modal image sets using large deformation minimum Kullback-Leibler divergence registration. The template that we generate is the class posterior that requires the least amount of deformation energy to be transformed into every class posterior density (each characterizing a multi-modal image set). This method is computationally practical; computation times grows linearly with the number of image sets. Template estimation results are presented for a set of five 3D class posterior images representing structures of the human brain.