Diffeomorphic density registration

In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite dimensional manifold find a diffeomorphism which transforms one to the other. This problem is motivated by the medical imaging application of tracking organ motion due to respiration in Thoracic CT imaging where the fundamental physical property of conservation of mass naturally leads to modeling CT attenuation as a density. We will study the intimate link between the Riemannian metrics on the space of diffeomorphisms and those on the space of densities. We finally develop novel computationally efficient algorithms and demonstrate there applicability for registering RCCT thoracic imaging.Comment: 23 pages, 6 Figures, Chapter for a Book on Medical Image Analysi

Weighted Diffeomorphic Density Matching with Applications to Thoracic Image Registration

In this article we study the problem of thoracic image registration, in particular the estimation of complex anatomical deformations associated with the breathing cycle. Using the intimate link between the Riemannian geometry of the space of diffeomorphisms and the space of densities, we develop an image registration framework that incorporates both the fundamental law of conservation of mass as well as spatially varying tissue compressibility properties. By exploiting the geometrical structure, the resulting algorithm is computationally efficient, yet widely general.Comment: Accepted in Proceedings of the 5th MICCAI workshop on Mathematical Foundations of Computational Anatomy, Munich, Germany, 2015 (http://www-sop.inria.fr/asclepios/events/MFCA15/

Segmentation, tracking, and kinematics of lung parenchyma and lung tumors from 4D CT with application to radiation treatment planning.

This thesis is concerned with development of techniques for efficient computerized analysis of 4-D CT data. The goal is to have a highly automated approach to segmentation of the lung boundary and lung nodules inside the lung. The determination of exact lung tumor location over space and time by image segmentation is an essential step to track thoracic malignancies. Accurate image segmentation helps clinical experts examine the anatomy and structure and determine the disease progress. Since 4-D CT provides structural and anatomical information during tidal breathing, we use the same data to also measure mechanical properties related to deformation of the lung tissue including Jacobian and strain at high resolutions and as a function of time. Radiation Treatment of patients with lung cancer can benefit from knowledge of these measures of regional ventilation. Graph-cuts techniques have been popular for image segmentation since they are able to treat highly textured data via robust global optimization, avoiding local minima in graph based optimization. The graph-cuts methods have been used to extract globally optimal boundaries from images by s/t cut, with energy function based on model-specific visual cues, and useful topological constraints. The method makes N-dimensional globally optimal segmentation possible with good computational efficiency. Even though the graph-cuts method can extract objects where there is a clear intensity difference, segmentation of organs or tumors pose a challenge. For organ segmentation, many segmentation methods using a shape prior have been proposed. However, in the case of lung tumors, the shape varies from patient to patient, and with location. In this thesis, we use a shape prior for tumors through a training step and PCA analysis based on the Active Shape Model (ASM). The method has been tested on real patient data from the Brown Cancer Center at the University of Louisville. We performed temporal B-spline deformable registration of the 4-D CT data - this yielded 3-D deformation fields between successive respiratory phases from which measures of regional lung function were determined. During the respiratory cycle, the lung volume changes and five different lobes of the lung (two in the left and three in the right lung) show different deformation yielding different strain and Jacobian maps. In this thesis, we determine the regional lung mechanics in the Lagrangian frame of reference through different respiratory phases, for example, Phase10 to 20, Phase10 to 30, Phase10 to 40, and Phase10 to 50. Single photon emission computed tomography (SPECT) lung imaging using radioactive tracers with SPECT ventilation and SPECT perfusion imaging also provides functional information. As part of an IRB-approved study therefore, we registered the max-inhale CT volume to both VSPECT and QSPECT data sets using the Demon\u27s non-rigid registration algorithm in patient subjects. Subsequently, statistical correlation between CT ventilation images (Jacobian and strain values), with both VSPECT and QSPECT was undertaken. Through statistical analysis with the Spearman\u27s rank correlation coefficient, we found that Jacobian values have the highest correlation with both VSPECT and QSPECT

3-D lung deformation and function from respiratory-gated 4-D x-ray CT images : application to radiation treatment planning.

Many lung diseases or injuries can cause biomechanical or material property changes that can alter lung function. While the mechanical changes associated with the change of the material properties originate at a regional level, they remain largely asymptomatic and are invisible to global measures of lung function until they have advanced significantly and have aggregated. In the realm of external beam radiation therapy of patients suffering from lung cancer, determination of patterns of pre- and post-treatment motion, and measures of regional and global lung elasticity and function are clinically relevant. In this dissertation, we demonstrate that 4-D CT derived ventilation images, including mechanical strain, provide an accurate and physiologically relevant assessment of regional pulmonary function which may be incorporated into the treatment planning process. Our contributions are as follows: (i) A new volumetric deformable image registration technique based on 3-D optical flow (MOFID) has been designed and implemented which permits the possibility of enforcing physical constraints on the numerical solutions for computing motion field from respiratory-gated 4-D CT thoracic images. The proposed optical flow framework is an accurate motion model for the thoracic CT registration problem. (ii) A large displacement landmark-base elastic registration method has been devised for thoracic CT volumetric image sets containing large deformations or changes, as encountered for example in registration of pre-treatment and post-treatment images or multi-modality registration. (iii) Based on deformation maps from MOFIO, a novel framework for regional quantification of mechanical strain as an index of lung functionality has been formulated for measurement of regional pulmonary function. (iv) In a cohort consisting of seven patients with non-small cell lung cancer, validation of physiologic accuracy of the 4-0 CT derived quantitative images including Jacobian metric of ventilation, Vjac, and principal strains, (V?1, V?2, V?3, has been performed through correlation of the derived measures with SPECT ventilation and perfusion scans. The statistical correlations with SPECT have shown that the maximum principal strain pulmonary function map derived from MOFIO, outperforms all previously established ventilation metrics from 40-CT. It is hypothesized that use of CT -derived ventilation images in the treatment planning process will help predict and prevent pulmonary toxicity due to radiation treatment. It is also hypothesized that measures of regional and global lung elasticity and function obtained during the course of treatment may be used to adapt radiation treatment. Having objective methods with which to assess pre-treatment global and regional lung function and biomechanical properties, the radiation treatment dose can potentially be escalated to improve tumor response and local control

GIFTed Demons: deformable image registration with local structure-preserving regularization using supervoxels for liver applications.

Deformable image registration, a key component of motion correction in medical imaging, needs to be efficient and provides plausible spatial transformations that reliably approximate biological aspects of complex human organ motion. Standard approaches, such as Demons registration, mostly use Gaussian regularization for organ motion, which, though computationally efficient, rule out their application to intrinsically more complex organ motions, such as sliding interfaces. We propose regularization of motion based on supervoxels, which provides an integrated discontinuity preserving prior for motions, such as sliding. More precisely, we replace Gaussian smoothing by fast, structure-preserving, guided filtering to provide efficient, locally adaptive regularization of the estimated displacement field. We illustrate the approach by applying it to estimate sliding motions at lung and liver interfaces on challenging four-dimensional computed tomography (CT) and dynamic contrast-enhanced magnetic resonance imaging datasets. The results show that guided filter-based regularization improves the accuracy of lung and liver motion correction as compared to Gaussian smoothing. Furthermore, our framework achieves state-of-the-art results on a publicly available CT liver dataset

A biomechanical approach for real-time tracking of lung tumors during External Beam Radiation Therapy (EBRT)

Lung cancer is the most common cause of cancer related death in both men and women. Radiation therapy is widely used for lung cancer treatment. However, this method can be challenging due to respiratory motion. Motion modeling is a popular method for respiratory motion compensation, while biomechanics-based motion models are believed to be more robust and accurate as they are based on the physics of motion. In this study, we aim to develop a biomechanics-based lung tumor tracking algorithm which can be used during External Beam Radiation Therapy (EBRT). An accelerated lung biomechanical model can be used during EBRT only if its boundary conditions (BCs) are defined in a way that they can be updated in real-time. As such, we have developed a lung finite element (FE) model in conjunction with a Neural Networks (NNs) based method for predicting the BCs of the lung model from chest surface motion data. To develop the lung FE model for tumor motion prediction, thoracic 4D CT images of lung cancer patients were processed to capture the lung and diaphragm geometry, trans-pulmonary pressure, and diaphragm motion. Next, the chest surface motion was obtained through tracking the motion of the ribcage in 4D CT images. This was performed to simulate surface motion data that can be acquired using optical tracking systems. Finally, two feedforward NNs were developed, one for estimating the trans-pulmonary pressure and another for estimating the diaphragm motion from chest surface motion data. The algorithm development consists of four steps of: 1) Automatic segmentation of the lungs and diaphragm, 2) diaphragm motion modelling using Principal Component Analysis (PCA), 3) Developing the lung FE model, and 4) Using two NNs to estimate the trans-pulmonary pressure values and diaphragm motion from chest surface motion data. The results indicate that the Dice similarity coefficient between actual and simulated tumor volumes ranges from 0.76±0.04 to 0.91±0.01, which is favorable. As such, real-time lung tumor tracking during EBRT using the proposed algorithm is feasible. Hence, further clinical studies involving lung cancer patients to assess the algorithm performance are justified