Gary E. Christensen

Deformable templates using large deformation kinematics

A general automatic approach is presented for accommodating local shape variation when mapping a two-dimensional (2-D) or three-dimensional (3-D) template image into alignment with a topologically similar target image. Local shape variability is accommodated by applying a vector-field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth (globally positive definite Jacobian). Smoothness is guaranteed without specifically penalizing large-magnitude deformations of small subvolumes by constraining the transformation on the basis of a Stokesian limit of the fluid-dynamical Navier-Stokes equations. This differs fundamentally from quadratic penalty methods, such as those based on linearized elasticity or thin-plate splines, in that stress restraining the motion relaxes over time allowing large-magnitude deformations. Kinematic nonlinearities are inherently necessary to maintain continuity of structures during large-magnitude deformations, and are included in all results. After initial global registration, final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem. Automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular. Application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability.

Consistent image registration

Presents a new method for image registration based on jointly estimating the forward and reverse transformations between two images while constraining these transforms to be inverses of one another. This approach produces a consistent set of transformations that have less pairwise registration error, i.e., better correspondence, than traditional methods that estimate the forward and reverse transformations independently. The transformations are estimated iteratively and are restricted to preserve topology by constraining them to obey the laws of continuum mechanics. The transformations are parameterized by a Fourier series to diagonalize the covariance structure imposed by the continuum mechanics constraints and to provide a computationally efficient numerical implementation. Results using a linear elastic material constraint are presented using both magnetic resonance and X-ray computed tomography image data. The results show that the joint estimation of a consistent set of forward and reverse transformations constrained by linear-elasticity give better registration results than using either constraint alone or none at all.

Volumetric transformation of brain anatomy

Presents diffeomorphic transformations of three-dimensional (3-D) anatomical image data of the macaque occipital lobe and whole brain cryosection imagery and of deep brain structures in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner, accommodating both global and local anatomical detail. The initial low-dimensional registration is accomplished by constraining the transformation to be in a low-dimensional basis. The basis is defined by the Greens function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The high-dimensional large deformations are vector fields generated via the mismatch between the template and target-image volumes constrained to be the solution of a Navier-Stokes fluid model. As part of this procedure, the Jacobian of the transformation is tracked, insuring the generation of diffeomorphisms. It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration.

A method for the reconstruction of four-dimensional synchronized CT scans acquired during free breathing

Breathing motion is a significant source of error in radiotherapy treatment planning for the thorax and upper abdomen. Accounting for breathing motion has a profound effect on the size of conformal radiation portals employed in these sites. Breathing motion also causes artifacts and distortions in treatment planning computed tomography (CT) scans acquired during free breathing and also causes a breakdown of the assumption of the superposition of radiation portals in intensity-modulated radiation therapy, possibly leading to significant dose delivery errors. Proposed voluntary and involuntary breath-hold techniques have the potential for reducing or eliminating the effects of breathing motion, however, they are limited in practice, by the fact that many lung cancer patients cannot tolerate holding their breath. We present an alternative solution to accounting for breathing motion in radiotherapy treatment planning, where multislice CT scans are collected simultaneously with digital spirometry over many free breathing cycles to create a four-dimensional (4-D) image set, where tidal lung volume is the additional dimension. An analysis of this 4-D data leads to methods for digital-spirometry, based elimination or accounting of breathing motion artifacts in radiotherapy treatment planning for free breathing patients. The 4-D image set is generated by sorting free-breathing multislice CT scans according to user-defined tidal-volume bins. A multislice CT scanner is operated in the ciné mode, acquiring 15 scans per couch position, while the patient undergoes simultaneous digital-spirometry measurements. The spirometry is used to retrospectively sort the CT scans by their correlated tidal lung volume within the patients normal breathing cycle. This method has been prototyped using data from three lung cancer patients. The actual tidal lung volumes agreed with the specified bin volumes within standard deviations ranging between 22 and 33 cm3. An analysis of sagittal and coronal images demonstrated relatively small (<1 cm) motion artifacts along the diaphragm, even for tidal volumes where the rate of breathing motion is greatest. While still under development, this technology has the potential for revolutionizing the radiotherapy treatment planning for the thorax and upper abdomen.

Consistent landmark and intensity-based image registration

Two new consistent image registration algorithms are presented: one is based on matching corresponding landmarks and the other is based on matching both landmark and intensity information. The consistent landmark and intensity registration algorithm produces good correspondences between images near landmark locations by matching corresponding landmarks and away from landmark locations by matching the image intensities. In contrast to similar unidirectional algorithms, these new consistent algorithms jointly estimate the forward and reverse transformation between two images while minimizing the inverse consistency error-the error between the forward (reverse) transformation and the inverse of the the reverse (forward) transformation. This reduces the ambiguous correspondence between the forward and reverse transformations associated with large inverse consistency errors. In both algorithms a thin-plate spline (TPS) model is used to regularize the estimated transformations. Two-dimensional (2-D) examples are presented that show the inverse consistency error produced by the traditional unidirectional landmark TPS algorithm can be relatively large and that this error is minimized using the consistent landmark algorithm. Results using 2-D magnetic resonance imaging data are presented that demonstrate that using landmark and intensity information together produce better correspondence between medical images than using either landmarks or intensity information alone.

3D brain mapping using a deformable neuroanatomy

This paper presents two different mathematical methods that can be used separately or in conjunction to accommodate shape variabilities between normal human neuroanatomies. Both methods use a digitized textbook to represent the complex structure of a typical normal neuroanatomy. Probabilistic transformations on the textbook coordinate system are defined to accommodate shape differences between the textbook and images of other normal neuroanatomies. The transformations are constrained to be consistent with the physical properties of deformable elastic solids in the first method and those of viscous fluids in the second. Results presented in this paper demonstrate how a single deformable textbook can be used to accommodate normal shape variability.

Evaluation of Registration Methods on Thoracic CT: The EMPIRE10 Challenge

EMPIRE10 (Evaluation of Methods for Pulmonary Image REgistration 2010) is a public platform for fair and meaningful comparison of registration algorithms which are applied to a database of intra patient thoracic CT image pairs. Evaluation of nonrigid registration techniques is a nontrivial task. This is compounded by the fact that researchers typically test only on their own data, which varies widely. For this reason, reliable assessment and comparison of different registration algorithms has been virtually impossible in the past. In this work we present the results of the launch phase of EMPIRE10, which comprised the comprehensive evaluation and comparison of 20 individual algorithms from leading academic and industrial research groups. All algorithms are applied to the same set of 30 thoracic CT pairs. Algorithm settings and parameters are chosen by researchers expert in the con figuration of their own method and the evaluation is independent, using the same criteria for all participants. All results are published on the EMPIRE10 website (http://empire10.isi.uu.nl). The challenge remains ongoing and open to new participants. Full results from 24 algorithms have been published at the time of writing. This paper details the organization of the challenge, the data and evaluation methods and the outcome of the initial launch with 20 algorithms. The gain in knowledge and future work are discussed.

Registration-based estimates of local lung tissue expansion compared to xenon CT measures of specific ventilation

The main function of the respiratory system is gas exchange. Since many disease or injury conditions can cause biomechanical or material property changes that can alter lung function, there is a great interest in measuring regional lung ventilation and regional specific volume change. We describe a registration-based technique for estimating local lung expansion from multiple respiratory-gated CT images of the thorax. The degree of regional lung expansion is measured using the Jacobian (a function of local partial derivatives) of the registration displacement field, which we show is directly related to specific volume change. We compare the ventral-dorsal patterns of lung expansion estimated across five pressure changes to a xenon CT based measure of specific ventilation in five anesthetized sheep studied in the supine orientation. Using 3D image registration to match images acquired at 10 cm H(2)O and 15 cm H(2)O airway pressures gave the best match between the average Jacobian and the xenon CT specific ventilation (linear regression, average r(2)=0.73).

Retrospective evaluation of intersubject brain registration

Although numerous methods to register brains of different individuals have been proposed, no work has been done, as far as we know, to evaluate and objectively compare the performances of different nonrigid (or elastic) registration methods on the same database of subjects. In this paper, we propose an evaluation framework, based on global and local measures of the relevance of the registration. We have chosen to focus more particularly on the matching of cortical areas, since intersubject registration methods are dedicated to anatomical and functional normalization, and also because other groups have shown the relevance of such registration methods for deep brain structures. Experiments were conducted using 6 methods on a database of 18 subjects. The global measures used show that the quality of the registration is directly related to the transformations degrees of freedom. More surprisingly, local measures based on the matching of cortical sulci did not show significant differences between rigid and non rigid methods.

Statistical methods in computational anatomy

This paper reviews recent developments by the Washington/Brown groups for the study of anatomical shape in the emerging new discipline of computational anatomy. Parametric representations of anatomical variation for computational anatomy are reviewed, restricted to the assumption of small deformations. The generation of covariance operators for probabilistic measures of anatomical variation on coordinatized submanifolds is formulated as an empirical procedure. Populations of brains are mapped to common coordinate systems, from which template coordinate systems are constructed which are closest to the population of anatomies in a minimum distance sense. Variation of several one-, two and three-dimensional manifolds, i.e. sulci, surfaces and brain volumes are examined via Gaussian measures with mean and covariances estimated directly from maps of templates to targets. Methods are presented for estimating the covariances of vector fields from a family of empirically generated maps, posed as generalized spectrum estimation indexed over the submanifolds. Covariance estimation is made parametric, analogous to autoregressive modelling, by introducing small deformation linear operators for constraining the spectrum of the fields.