Four-dimensional computed tomography (4DCT) is regularly used to visualize tumor motion in radiation therapy for lung cancer. These 4DCT images can be analyzed to estimate local ventilation by finding a dense correspondence map between the end inhalation and the end exhalation CT image volumes using deformable image registration. Lung regions with ventilation values above a threshold are labeled as regions of high pulmonary function and are avoided when possible in the radiation plan. This paper investigates a sensitivity analysis of the relative Jacobian error to small registration errors. We present a linear approximation of the relative Jacobian error. Next, we give a formula for the sensitivity of the relative Jacobian error with respect to the Jacobian of perturbation displacement field. Preliminary sensitivity analysis results are presented using 4DCT scans from 10 individuals. For each subject, we generated 6400 random smooth biologically plausible perturbation vector fields using a cubic B-spline model. We showed that the correlation between the Jacobian determinant and the Frobenius norm of the sensitivity matrix is close to -1, which implies that the relative Jacobian error in high-functional regions is less sensitive to noise. We also showed that small displacement errors on the average of 0.53 mm may lead to a 10% relative change in Jacobian determinant. We finally showed that the average relative Jacobian error and the sensitivity of the system for all subjects are positively correlated (close to +1), i.e. regions with high sensitivity has more error in Jacobian determinant on average.
MOTIVATION: The lobes of the lungs slide relative to each other during breathing. Quantifying lobar sliding can aid in
better understanding lung function, better modeling of lung dynamics, and a better understanding of the limits of image
registration performance near fissures. We have developed a method to estimate lobar sliding in the lung from image
registration of CT scans.
METHODS: Six human lungs were analyzed using CT scans spanning functional residual capacity (FRC) to total lung
capacity (TLC). The lung lobes were segmented and registered on a lobe-by-lobe basis. The displacement fields from the
independent lobe registrations were then combined into a single image. This technique allows for displacement
discontinuity at lobar boundaries. The displacement field was then analyzed as a continuum by forming finite elements
from the voxel grid of the FRC image. Elements at a discontinuity will appear to have undergone significantly elevated
'shear stretch' compared to those within the parenchyma. Shear stretch is shown to be a good measure of sliding
magnitude in this context.
RESULTS: The sliding map clearly delineated the fissures of the lung. The fissure between the right upper and right
lower lobes showed the greatest sliding in all subjects while the fissure between the right upper and right middle lobe
showed the least sliding.
Radiation induced pulmonary diseases can change the tissue material properties of lung parenchyma and the
mechanics of the respiratory system. Recent advances in multi-detector-row CT (MDCT), 4DCT respiratory
gating methods, and image processing techniques enable us to follow and measure those changes noninvasively
during radiation therapy at a regional level. This study compares the 4DCT based ventilation measurement with
the results from hyperpolarized helium-3 MR using the cumulative distribution function maps and the relative
overlap (RO) statistic. We show that the similarity between the two measurements increases as the increase of
the B-Spline grid spacing and Laplacian weighting which result a smoother ventilation map. The best similarity
is found with weighting of 0.5 for linear elasticity and B-Spline grid spacing of 32 mm. Future work is to improve
the lung image registration algorithm by incorporating hyperpolarized helium-3 MR information so as to improve
its physiological modeling of the lung tissue deformation.
Evaluating non-rigid image registration algorithm performance is a difficult problem since there is rarely a "gold
standard" (i.e., known) correspondence between two images. This paper reports the analysis and comparison
of five non-rigid image registration algorithms using the Non-Rigid Image Registration Evaluation Project
(NIREP) (www.nirep.org) framework. The NIREP framework evaluates registration performance using centralized
databases of well-characterized images and standard evaluation statistics (methods) which are implemented
in a software package. The performance of five non-rigid registration algorithms (Affine, AIR, Demons, SLE and
SICLE) was evaluated using 22 images from two NIREP neuroanatomical evaluation databases. Six evaluation
statistics (relative overlap, intensity variance, normalized ROI overlap, alignment of calcarine sulci, inverse consistency
error and transitivity error) were used to evaluate and compare image registration performance. The
results indicate that the Demons registration algorithm produced the best registration results with respect to the
relative overlap statistic but produced nearly the worst registration results with respect to the inverse consistency
statistic. The fact that one registration algorithm produced the best result for one criterion and nearly the worst
for another illustrates the need to use multiple evaluation statistics to fully assess performance.
In registration-based analyses of lung biomechanics and function, high quality registrations are essential to obtain
meaningful results. Various criteria have been suggested to find the correspondence mappings between two lung
images acquired at different levels of inflation. In this paper, we describe a new metric, the sum of squared
vesselness measure difference (SSVMD), that utilizes the rich information of blood vessel locations and matches
similar vesselness patterns in two images. Preserving both the lung tissue volume and the vesselness measure,
a registration algorithm is developed to minimize the sum of squared tissue volume difference (SSTVD) and
SSVMD together. We compare the registration accuracy using SSTVD + SSVMD with that using SSTVD
alone by registering lung CT images of three normal human subjects. After adding the new SSVMD metric, the
improvement of registration accuracy is observed by landmark error and fissure positioning error analyses. The
average values of landmark error and fissure positioning error are reduced by about 30% and 25%, respectively.
The mean landmark error is on the order of 1 mm. Statistical testing of landmark errors shows that there
is a statistically significant difference between two methods with p values < 0.05 in all three subjects. Visual
inspection shows there are obvious accuracy improvements in the lung regions near the thoracic cage after adding
SSVMD.
A queryable electronic atlas was developed to quantitatively characterize the normal human
lung airway tree and to provide a better understanding of the lung for diagnosing diseases and
evaluating treatments. The atlas consists of airway measurements taken from CT images using
the Pulmonary Workstation II (PW2) software package. These measurements include airway
cross-sectional area at midpoint between branch points; maximum and minimum diameter of
a particular airway cross section at segment midpoint; average, maximum, and minimum wall
thickness per branch; and wall thickness uniformity within a branch. The atlas provides user
friendly interfaces for interrogating population statistics, comparing populations, comparing
individuals to populations, and comparing individuals to other individuals. Populations can be
selected based on age, gender, race, ethnicity, and normalcy/disease.
The lungs undergo expansion and contraction during the respiratory cycle. Since many disease or injury conditions
are associated with the biomechanical or material property changes that can alter lung function, there is a
great interest in measuring regional lung ventilation and regional mechanical changes. We describe a technique
that uses multiple respiratory-gated CT images and non-rigid 3D image registration to make local estimates
of lung tissue expansion. The degree of regional lung expansion is measured using the Jacobian (a function
of local partial derivatives) of the registration displacement field. We compare the ventral-dorsal patterns of
lung expansion estimated in both retrospectively reconstructed dynamic scans and static breath-hold scans to
a xenon CT based measure of specific ventilation and a semi-automatic reference standard in four anesthetized
sheep studied in the supine orientation. The regional lung expansion estimated by 3D image registration of
images acquired at 50% and 75% phase points of the inspiratory portion of the respiratory cycle and 20 cm H2O
and 25 cm H2O airway pressures gave the best match between the average Jacobian and the xenon CT specific
ventilation respectively (linear regression, average r2 = 0.85 and r2 = 0.84). The registration accuracy assessed
by 200 semi-automatically matched landmarks in both the dynamic and static scans show landmark error on the
order of 2 mm.
Identifying the three-dimensional content of non-small cell lung cancer tumors is a vital step in the pursuit of
understanding cancer growth, development and response to treatment. The majority of non-small cell lung cancer
tumors are histologically heterogeneous, and consist of the malignant tumor cells, necrotic tumor cells, fibroblastic
stromal tissue, and inflammation. Geometric and tissue density heterogeneity are utilized in computed tomography (CT)
representations of lung tumors for distinguishing between malignant and benign nodules. However, the correlation
between radiolographical heterogeneity and corresponding histological content has been limited. In this study, a
multimodality dataset of human lung cancer is established, enabling the direct comparison between histologically
identified tissue content and micro-CT representation. Registration of these two datasets is achieved through the
incorporation of a large scale, serial microscopy dataset. This dataset serves as the basis for the rigid and non-rigid
registrations required to align the radiological and histological data. The resulting comprehensive, three-dimensional
dataset includes radio-density, color and cellular content of a given lung tumor. Using the registered datasets, neural
network classification is applied to determine a statistical separation between cancerous and non-cancerous tumor
regions in micro-CT.
Recent advancements in digital medical imaging have opened avenues for quantitative analyses of different volumetric
and morphometric indices in response to a disease or a treatment. However, a major challenge in performing such an
analysis is the lack of a technology of building a mean anatomic space (MAS) that allows mapping data of a given
subject onto MAS. This approach leads to a tool for point-by-point regional analysis and comparison of quantitative
indices for data coming from a longitudinal or transverse study. Toward this goal, we develop a new computation
technique, called Active Index Model (AIM), which is a unique tool to solve the stated problem. AIM consists of three
building blocks - (1) development of MAS for a particular anatomic site, (2) mapping a specific data onto MAS, (3)
regional statistical analysis of data from different populations assessing regional response to a disease or treatment
progression. The AIM presented here is built at the training phase from two known populations (e.g., normal and
diseased) which will be immediately ready for diagnostic purpose in a subject whose clinical status is unknown. AIM
will be useful for both cross sectional and longitudinal studies and for early diagnostic. This technique will be a vital
tool for understanding regional response of a disease or treatment at various stages of its progression. This method has
been applied for analyzing regional trabecular bone structural distribution in rabbit femur via micro-CT imaging and to
localize the affected myocardial regions from cardiac MR data.
Respiratory motion is a significant source of error in conformal radiation therapy for the thorax and upper abdomen. Four-dimensional computed tomography (4D CT) has been proposed to reduce the uncertainty caused by internal respiratory organ motion. A 4D CT dataset is retrospectively reconstructed at various stages of a respiratory cycle. An important tool for 4D treatment planning is deformable image registration. An inverse consistent image registration is used to model lung motion from one respiratory stage to another during a breathing cycle. This diffeomorphic registration jointly estimates the forward and reverse transformations providing more accurate correspondence between two images. Registration results and modeled motions in the lung are shown for three example respiratory stages. The results demonstrate that the consistent image registration satisfactorily models the large motions in the lung, providing a useful tool for 4D planning and delivering.
A method is described to estimate regional lung expansion and related biomechanical parameters using multiple CT images of the lungs, acquired at different inflation levels. In this study, the lungs of two sheep were imaged utilizing a multi-detector row CT at different lung inflations in the prone and supine positions. Using the lung surfaces and the airway branch points for guidance, a 3D inverse consistent image registration procedure was used to match different lung volumes at each orientation. The registration was validated using a set of implanted metal markers. After registration, the Jacobian of the deformation field was computed to express regional expansion or contraction. The regional lung expansion at different pressures and different orientations are compared.
Issam El Naqa, Daniel Low, Gary Christensen, Parag Parikh, Joo Hyun Song, Michelle Nystrom, Wei Lu, Joseph Deasy, James Hubenschmidt, Sasha Wahab, Sasa Mutic, Anurag Singh, Jeffrey Bradley
We are developing 4D-CT to provide breathing motion information (trajectories) for radiation therapy treatment planning of lung cancer. Potential applications include optimization of intensity-modulated beams in the presence of breathing motion and intra-fraction target volume margin determination for conformal therapy. The images are acquired using a multi-slice CT scanner while the patient undergoes simultaneous quantitative spirometry. At each couch position, the CT scanner is operated in ciné mode and acquires up to 15 scans of 12 slices each. Each CT scan is associated with the measured tidal volume for retrospective reconstruction of 3D CT scans at arbitrary tidal volumes. The specific tasks of this project involves the development of automated registration of internal organ motion (trajectories) during breathing. A modified least-squares based optical flow algorithm tracks specific features of interest by modifying the eigenvalues of gradient matrix (gradient structural tensor). Good correlations between the measured motion and spirometry-based tidal volume are observed and evidence of internal hysteresis is also detected.
This paper provides initial analysis of a new consistent, large-deformation elastic image registration (CLEIR) algorithm that jointly estimates a consistent set of forward and reverse transformations between two images. The estimated transformations are able to accommodate large deformations while constraining the forward and reverse transformations to be inverses of one another. The algorithm assumes that the two N-dimensional images to be registered contain topologically similar objects and were collected using the same imaging modality. The image registration problem is formulated in a (N+1)-dimensional space where the additional dimension is referred to as the temporal or time dimension. A periodic-in-time, nonlinear, (N+1)-dimensional transformation is estimated that deforms one image into the shape of the other and back again. Large deformations from one image to the other are accommodated by concatenating the small-deformation incremental transformations from one time instant to the next. An inverse consistency constraint is placed on the incremental transformations to enforce within a specified tolerance that the forward and reverse transformations between the two images are inverses of each other. The feasibility of the algorithm for accommodating nonlinear deformations was demonstrated using 2D synthesized phantom images and CT inner ear images. The effect of varying the number of intermediate templates was studied for these data sets.
CT can be used to study pulmonary structure-function relationships. There is a growing clinical need to match pulmonary structures across individuals to detect abnormal structure due to disease and to compare regional pulmonary function. In this paper, we propose a novel scheme for registering and warping 3-D pulmonary CT images of different subjects in two main steps: 1) identify a set of reproducible feature points for each CT image to establish correspondences across subjects; 2) use a landmark and intensity-based consistent image registration algorithm to warp a template image volume to the rest of the lung volumes. Effectiveness of the proposed scheme is evaluated and visualized using both gray-level and segmented CT images. Results show that the proposed scheme is able to reduce landmark registration error and relative volume overlapping error from 10.5 mm and 0.70 before registration to 0.4 mm and 0.11, respectively. The proposed scheme can be used to construct a computerized human lung model (or atlas) to help detect abnormal lung structural changes.
Establishing the average shape and spatial variability for a set of similar anatomical objects is important for detecting and discriminating morphological differences between populations. This may be done using deformable templates to synthesize a 3D CT/MRI image of the average anatomy from a set of CT/MRI images collected from a population of similar anatomical objects. This paper investigates the error associated with the choice of template selected from the population used to synthesize the average population shape. Population averages were synthesized for a population of five infant skulls with sagittal synostosis and a population of six normal adult brains using a consistent linear-elastic image registration algorithm. Each data set from the populations was used as the template to synthesize a population average. This resulted in five different population averages for the skull population and six different population averages for the brain population. The displacement variance distance from a skull within the population to the other skulls in the population ranged from 5.5 to 9.9 mm2 while the displacement variance distance from the synthesized average skulls to the population ranged from 2.2 to 2.7 mm2. The displacement variance distance from a brain within the population to the other brains in the population ranged from 9.3 to 14.2 mm2 while the displacement variance distance from the synthesized average brains to the population ranged from 3.2 to 3.6 mm2. These results suggest that there was no significant difference between the choice of template with respect to the shape of the synthesized average data set for these two populations.
Registration of anatomical images is useful for many applications including image segmentation, characterization of normal and abnormal shape, and creating deformable anatomical shape atlases. The usefulness of the information derived from image registration depends on the degree of anatomically meaningful correspondence between the images. We assume that an ideal image registration algorithm can determine an unique correspondence mapping between any two image volumes imaged from a homogeneous population of anatomies; and that these transformations have the properties of invertibility and transitivity. Unfortunately, current image registration algorithms are far from ideal. In this paper we test the invertibility and transitivity of transformations computed from a 'traditional' and a consistent linear-elastic registration algorithm. Invertibility of the transformations was evaluated by comparing the composition of transformations from image A-to-B and B-to-A to the identity mapping. Transitivity of the transformations was evaluated by measuring the difference between the identity mapping and the composition the transformations from image A-to-B, B-to-C, and C-to-A. Transformations were generated by matching computer generated phantoms, CT data of infant heads, and MRI data of adult brains. The consistent algorithm out performed the 'traditional' algorithm by 8 to 16 times for the invertibility test and 2 to 5 times for the transitivity test.
KEYWORDS: Brain, Magnetic resonance imaging, Skull, Medical imaging, Computed tomography, 3D image processing, Neuroimaging, 3D acquisition, 3D modeling, Nose
A major task in diagnostic medicine is to determine whether or not an individual has a normal or abnormal anatomy by examining medical images such as MRI, CT, etc. Unfortunately, there are few quantitative measures that a physician can use to discriminate between normal and abnormal besides a couple of length, width, height, and volume measurements. In fact, there is no definition/picture of what normal anatomical structures--such as the brain-- look like let alone normal anatomical variation. The goal of this work is to synthesize average 3D anatomical shapes using deformable templates. We present a method for empirically estimating the average shape and variation of a set of 3D medical image data sets collected from a homogeneous population of topologically similar anatomies. Results are shown for synthesizing the average brain image volume from a set of six normal adults and synthesizing the average skull/head image volume from a set of five 3 - 4 month old infants with sagittal synostosis.
Left/right craniofacial asymmetry is typically measured by comparing distances between standard anatomical landmarks. However, these measurements are of limited use for visualizing and quantifying the asymmetry at non-landmark locations. This work presents a method for calculating, measuring and visualizing the planar deviation of the midsagittal surface for the purpose of craniofacial dysmorphology assessment, pre-operative corrective surgery planning, and post-operative evaluation. A set of midsagittal landmarks are used to define a reference midsagittal plane and to define a non-planar surface that passes through the landmarks. The surface is modeled as a thin-plate spline that can be visualized in 3D using a virtual reality markup language browser and it can be fused with the original volume rendered CT data using VoxelViewTM.
This paper describes a new method to register serial, volumetric x-ray computed tomography (CT) data sets for tracking soft-tissue deformation caused by insertion of intracavity brachytherapy applicators to treat cervical cancer. 3D CT scans collected from the same patient with and without a brachytherapy applicator are registered to aid in computation of the radiation dose to tumor and normal tissue. The 3D CT image volume of pelvic anatomy with the applicator. Initial registration is accomplished by rigid alignment of the pelvic bones and non-rigid alignment of gray scale CT data and hand segmentations of the vagina, cervix, bladder, and rectum. A viscous fluid transformation model is used for non-rigid registration to allow for local, non-linear registration of the vagina, cervix, bladder, and rectum without disturbing the rigid registration of the bony pelvis and adjacent structures. Results are presented in which two 3D CT data sets of the same patient - imaged with and without a brachytherapy applicator - are registered.
In this paper we present a coarse-to-fine approach for the transformation of digital anatomical textbooks from the ideal to the individual that unifies the work on landmark deformations and volume based transformation. The Hierarchical approach is linked to the Biological problem itself, coming out of the various kinds of information which is provided by the anatomists. This information is in the form of points, lines, surfaces and sub-volumes corresponding to 0, 1, 2, and 3 dimensional sub-manifolds respectively. The algorithm is driven by these sub- manifolds. We follow the approach that the highest dimensional transformation is a result from the solution of a sequence of lower dimensional problems driven by successive refinements or partitions of the images into various Biologically meaningful sub-structures.
KEYWORDS: Chemical elements, Mechanics, Data modeling, Sensors, Optical sensors, Image sensors, Finite element methods, Medical imaging, Image registration, Associative arrays
In the current work we integrate well established techniques from finite deformation continuum mechanics with concepts from pattern recognition and image processing to develop a new finite element (FE) tool that combines image-based data with mechanics. Results track the deformation of material continua in the presence of unknown forces and/or material properties by using image-based data to provide the additional required information. The deformation field is determined from a variational problem that combines both the mechanics and models of the imaging sensors. A nonlinear FE approach is used to approximate the solution of the coupled problem. Results can be applied to (1) track the motion of deforming material and/or, (2) morphological warping of template images or patterns. 2D example results are provided for problems of the second type. One of the present examples was motivated primarily by a problem in medical imaging--mapping intersubject geometrical differences in human anatomical structures--with specific results given for the mapping 2D slices of the human distal femur based on X-ray computed tomographic images.
KEYWORDS: Image segmentation, Magnetic resonance imaging, Brain, Neuroimaging, 3D image processing, Head, Magnetism, Brain mapping, Scanning electron microscopy, Medicine
The precision and accuracy of area estimates from magnetic resonance (MR) brain images and using manual and automated segmentation methods are determined. Areas of the human hippocampus were measured to compare a new automatic method of segmentation with regions of interest drawn by an expert. MR images of nine normal subjects and nine schizophrenic patients were acquired with a 1.5-T unit (Siemens Medical Systems, Inc., Iselin, New Jersey). From each individual MPRAGE 3D volume image a single comparable 2-D slice (matrix equals 256 X 256) was chosen which corresponds to the same coronal slice of the hippocampus. The hippocampus was first manually segmented, then segmented using high dimensional transformations of a digital brain atlas to individual brain MR images. The repeatability of a trained rater was assessed by comparing two measurements from each individual subject. Variability was also compared within and between subject groups of schizophrenics and normal subjects. Finally, the precision and accuracy of automated segmentation of hippocampal areas were determined by comparing automated measurements to manual segmentation measurements made by the trained rater on MR and brain slice images. The results demonstrate the high repeatability of area measurement from MR images of the human hippocampus. Automated segmentation using high dimensional transformations from a digital brain atlas provides repeatability superior to that of manual segmentation. Furthermore, the validity of automated measurements was demonstrated by a high correlation with manual segmentation measurements made by a trained rater. Quantitative morphometry of brain substructures (e.g. hippocampus) is feasible by use of a high dimensional transformation of a digital brain atlas to an individual MR image. This method automates the search for neuromorphological correlates of schizophrenia by a new mathematically robust method with unprecedented sensitivity to small local and regional differences.
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