FEM-based evaluation of deformable image registration for radiation therapy

This paper presents a new concept to automatically detect the neighborhood in an image where deformable registration is mis-performing. Specifically, the displacement vector field (DVF) from a deformable image registration is substituted into a finite-element-based elastic framework to calculate unbalanced energy in each element. The value of the derived energy indicates the quality of the DVF in its neighborhood. The new voxel-based evaluation approach is compared with three other validation criteria: landmark measurement, a finite element approach and visual comparison, for deformable registrations performed with the optical-flow-based 'demons' algorithm as well as thin-plate spline interpolation. This analysis was performed on three pairs of prostate CT images. The results of the analysis show that the four criteria give mutually comparable quantitative assessments on the six registration instances. As an objective concept, the unbalanced energy presents no requirement on boundary constraints in its calculation, different from traditional mechanical modeling. This method is automatic, and at voxel level suitable to evaluate deformable registration in a clinical setting.     

Computerized method for nonrigid MR-to-PET breast-image registration

We have developed and tested a new simple computerized finite element method (FEM) approach to MR-to-PET nonrigid breast-image registration. The method requires five-nine fiducial skin markers (FSMs) visible in MRI and PET that need to be located in the same spots on the breast and two on the flanks during both scans. Patients need to be similarly positioned prone during MRI and PET scans. This is accomplished by means of a low gamma-ray attenuation breast coil replica used as the breast support during the PET scan. We demonstrate that, under such conditions, the observed FSM displacement vectors between MR and PET images, distributed piecewise linearly over the breast volume, produce a deformed FEM mesh that reasonably approximates nonrigid deformation of the breast tissue between the MRI and PET scans. This method, which does not require a biomechanical breast tissue model, is robust and fast. Contrary to other approaches utilizing voxel intensity-based similarity measures or surface matching, our method works for matching MR with pure molecular images (i.e. PET or SPECT only). Our method does not require a good initialization and would not be trapped by local minima during registration process. All processing including FSMs detection and matching, and mesh generation can be fully automated. We tested our method on MR and PET breast images acquired for 15 subjects. The procedure yielded good quality images with an average target registration error below 4 mm (i.e. well below PET spatial resolution of 6-7 mm). Based on the results obtained for 15 subjects studied to date, we conclude that this is a very fast and a well-performing method for MR-to-PET breast-image nonrigid registration. Therefore, it is a promising approach in clinical practice. This method can be easily applied to nonrigid registration of MRI or CT of any type of soft-tissue images to their molecular counterparts such as obtained using PET and SPECT.     

Automatic nonrigid registration of whole body CT mice images

Three-dimensional intra- and intersubject registration of image volumes is important for tasks that include quantification of temporal/longitudinal changes, atlas-based segmentation, computing population averages, or voxel and tensor-based morphometry. While a number of methods have been proposed to address this problem, few have focused on the problem of registering whole body image volumes acquired either from humans or small animals. These image volumes typically contain a large number of articulated structures, which makes registration more difficult than the registration of head images, to which the majority of registration algorithms have been applied. This article presents a new method for the automatic registration of whole body computed tomography (CT) volumes, which consists of two main steps. Skeletons are first brought into approximate correspondence with a robust point-based method. Transformations so obtained are refined with an intensity-based nonrigid registration algorithm that includes spatial adaptation of the transformation's stiffness. The approach has been applied to whole body CT images of mice, to CT images of the human upper torso, and to human head and neck CT images. To validate the authors method on soft tissue structures, which are difficult to see in CT images, the authors use coregistered magnetic resonance images. They demonstrate that the approach they propose can successfully register image volumes even when these volumes are very different in size and shape or if they have been acquired with the subjects in different positions.     

Accuracy and sensitivity of finite element model-based deformable registration of the prostate

PURPOSE: Evaluate the accuracy and the sensitivity to contour variation and model size of a finite element model-based deformable registration algorithm for the prostate. METHODS AND MATERIALS: Two magnetic resonance images (MRIs) were obtained for 21 prostate patients with three implanted markers. A single observer contoured the prostate and markers and performed blinded recontouring of the first MRI. A biomechanical-model based deformable registration algorithm, MORFEUS, was applied to each dataset pair, deforming the second image (B) to the first image (A). The residual error was calculated by comparing the center of mass (COM) of the markers with the predicted COM. Sensitivity to contour variation was calculated by deforming B to the repeat contour of A (A2). The sensitivity to the model size was calculated by reducing the number of nodes (B', A', A2') and repeating the analysis. RESULTS: The average residual error of the registration for B to A and B to A2 was 0.22 cm (SD: 0.08 cm) and 0.24 cm (SD: 0.09 cm), respectively. The average residual error of the registration of B' to A' and B' to A2' was 0.22 cm (SD: 0.10 cm) and 0.25 cm (SD: 0.10 cm), respectively. The average time to run MORFEUS on the standard and reduced model was 3606 s (SD: 7788 s) and 56 s (SD: 16 s), respectively. CONCLUSIONS: The accuracy of the algorithm, equal to the image voxel size, is not affected by intraobserver contour variability or model size. Reducing the model size significantly increases algorithm efficiency.     

A deformable image registration method to handle distended rectums in prostate cancer radiotherapy

In image-guided adaptive radiotherapy, it is important to have the capability to automatically and accurately delineate the rectal wall, which is a major dose-limiting organ in prostate cancer radiotherapy. As image registration is a process to find the spatial correspondence between two images, a major challenge in intensity-based deformable image registration is to deal with the situation where no correspondence exists for some objects between the two images to be registered. One example is the variation of rectal contents due to the presence and absence of bowel gas. The intensity-based deformable image registration methods alone cannot create the correct spatial transformation if there is no correspondence between the source and target images. In this study we implemented an automatic image intensity modification procedure to create artificial gas pockets in the planning computed tomography (CT) images. A diffusion-based deformable image registration algorithm was developed to use an adaptive smoothing algorithm to better handle large organ deformations. The process was tested in 15 prostate cancer cases and 30 daily CT images containing the largest distended rectums. The manually delineated rectums agreed well with the autodelineated rectums when using the image-intensity modification procedure.     

Assessment of dose reconstruction errors in image-guided radiation therapy

Dose reconstruction can be used to improve the accuracy of dose evaluation throughout a treatment course. Its working mechanism is based on deformable image registration (DIR). The purpose of this paper is to develop a method to estimate the dose reconstruction error associated with the inaccuracy of DIR algorithms. To reach this goal, we quantified dominant errors in DIR in terms of unbalanced energy (UE), which were compared with the standard displacement error (SDE). Their high similarity, characterized by Pearson correlation coefficient, was verified through nine 'demons' registration instances performed within simulated reference frames. Based on the similarity, the dose-warping discrepancy at each voxel was defined as a line integral of the dose gradient within the voxel's neighborhood whose boundary was determined by the voxel's UE value. From this definition, the dose reconstruction error was then calculated at each voxel on nine prostate computed tomography images, obtained from a patient treatment course. The average of the Pearson correlation coefficients between UE and SDE over the simulated registration instances was above 70%. The mean value of the dose reconstruction errors in a target volume was calculated for each of nine treatment fractions. The averaged percentage of these mean values with respect to the prescribed dose on the target volume was 1.68%. These results are consistent with contour-based mean dose error evaluations. This paper has established a relation between a registration error and its induced dose reconstruction discrepancy. It allows an automatic validation method to be developed to estimate the dose accumulation error at each voxel in clinical settings.     

Novel method to calculate pulmonary compliance images in rodents from computed tomography acquired at constant pressures

Our goal was to develop a method for generating high-resolution three-dimensional pulmonary compliance images in rodents from computed tomography (CT) images acquired at a series of constant pressures in ventilated animals. One rat and one mouse were used to demonstrate this technique. A pre-clinical GE flat panel CT scanner (maximum 31 line-pairs cm(-1) resolution) was utilized for image acquisition. The thorax of each animal was imaged with breath-holds at 2, 6, 10, 14 and 18 cm H2O pressure in triplicate. A deformable image registration algorithm was applied to each pair of CT images to map corresponding tissue elements. Pulmonary compliance was calculated on a voxel by voxel basis using adjacent pairs of CT images. Triplicate imaging was used to estimate the measurement error of this technique. The 3D pulmonary compliance images revealed regional heterogeneity of compliance. The maximum total lung compliance measured 0.080 (+/-0.007) ml air per cm H2O per ml of lung and 0.039 (+/-0.004) ml air per cm H2O per ml of lung for the rat and mouse, respectively. In this study, we have demonstrated a unique method of quantifying regional lung compliance from 4 to 16 cm H2O pressure with sub-millimetre spatial resolution in rodents.     

A hybrid framework for registration of carotid ultrasound images combining iconic and geometric features

Stroke is the third major cause of death worldwide behind heart disease and cancer. Carotid atherosclerosis is the most frequent cause of ischemic stroke. Early diagnosis of carotid plaque and serial monitoring of its size with the help of imaging modalities can help to prevent the atherosclerotic complications. The main difficulty is inevitable variability of patient’s head positions during image acquisitions. The time series registration of carotid images helps to improve the monitoring, characterization, and quantification of the disease by suppressing the global movements of the patient. In this work, a novel hybrid registration technique has been proposed and evaluated for registration of carotid ultrasound images taken at different times. The proposed hybrid method bridges the gap between the feature-based and intensity-based registration methods. The feature-based iterative closest point algorithm is used to provide a coarse registration which is subsequently refined by the intensity-based algorithm. The proposed framework uses rigid transformation model coupled with mutual information (MI) similarity measure and Powell optimizer. For quantitative evaluation, different registration approaches have been compared using four error metrics: visual information fidelity, structural similarity index, correlation coefficient, and MI. Qualitative evaluation has also been done using the visual examination of the registered image pairs.     

精确锥形束CT和扇形束CT三维变形配准

自适应放疗可根据患者解剖和/或生理的变化对放疗计划进行修正。与加速器集成的锥形束CT成像装置是最普遍的在线影像获取设备。但是,由于锥形束CT固有的电子散射,重建影像的电子密度不准确,使得通常采用的基于密度的配准算法配准计划扇形束CT和在线获取的锥形束CT影像时,会产生较大的配准误差。我们通过建模图像变形配准问题为一个求解梯度距离能量泛函的极值问题,然后通过变分法和Gauss-Seidel方法获得一种新型的基于梯度信息的变形配准算法的迭代公式。该方法在迭代过程中同时考虑梯度信息的吻合和变形场的连续性,产生准确光滑的变形场。此算法迭代公式的局部特性,使其便于并行实施。通过OpenCL编程将此算法在图形处理器(GPU)上并行实施,大大缩短了配准时间。利用配准结果结合flood filling和cubic matching算法,可以快速地完成在线器官映射。算法临床数据配准结果表明,本文提出的基于梯度场的配准算法与基于密度的算法相比可以更准确地配准临床锥形束CT和扇形束CT影像。由于配准可以在很短的时间内完成,配准结果可用于在线器官映射和在线重新计划优化。     

Performance of a feature-based algorithm for 3D-3D registration of CT angiography to cone-beam CT for endovascular repair of complex abdominal aortic aneurysms

Background

A crucial step in image fusion for intraoperative guidance during endovascular procedures is the registration of preoperative computed tomography angiography (CTA) with intraoperative Cone Beam CT (CBCT). Automatic tools for image registration facilitate the 3D image guidance workflow. However their performance is not always satisfactory. The aim of this study is to assess the accuracy of a new fully automatic, feature-based algorithm for 3D3D registration of CTA to CBCT.

Methods

The feature-based algorithm was tested on clinical image datasets from 14 patients undergoing complex endovascular aortic repair. Deviations in Euclidian distances between vascular as well as bony landmarks were measured and compared to an intensity-based, normalized mutual information algorithm.

Results

The results for the feature-based algorithm showed that the median 3D registration error between the anatomical landmarks of CBCT and CT images was less than 3 mm. The feature-based algorithm showed significantly better accuracy compared to the intensity-based algorithm (p?<?0.001).

Conclusion

A feature-based algorithm for 3D image registration is presented.

     

4D-CT lung motion estimation with deformable registration: quantification of motion nonlinearity and hysteresis

In this article, our goal is twofold. First, we propose and compare two methods which process deformable registration to estimate patient specific lung and tumor displacements and deformation during free breathing from four-dimensional computed tomography (4D-CT) data. Second, we propose techniques to quantify the physiological parameters of motion nonlinearity and hysteresis. A Fréchet distance-based criterion is introduced to measure the motion hysteresis. Experiments were conducted with 4D-CT data of five patients treated in radiotherapy for non-small cell lung cancer. The accuracy of deformation fields assessed against expert-selected landmarks was found to be within image voxel tolerance. The second method gave slightly better results in terms of accuracy and consistency, although the differences were not statistically significant between the two methods. Lung motion nonlinearity and hysteresis are patient specific, and vary across regions within the lung during respiration. For all patients, motion between end-exhale and end-inhale was well approximated with a straight line trajectory for the majority of lung points. Hysteresis was found to be globally correlated with trajectory length. The main limitation to the proposed method is that intensity-based deformable registration is dependent on image quality and image resolution. Another limitation is the absence of gold standard which makes the validation of the computed motion difficult. However, the proposed tools provide patient specific motion information which, in radiotherapy for example, can ease the definition of precise internal margins. In the future, the integration of physiological information from multiple patients could help to create a general lung atlas with different clinical applications.     

Image registration with auto-mapped control volumes

Many image registration algorithms rely on the use of homologous control points on the two input image sets to be registered. In reality, the interactive identification of the control points on both images is tedious, difficult, and often a source of error. We propose a two-step algorithm to automatically identify homologous regions that are used as a priori information during the image registration procedure. First, a number of small control volumes having distinct anatomical features are identified on the model image in a somewhat arbitrary fashion. Instead of attempting to find their correspondences in the reference image through user interaction, in the proposed method, each of the control regions is mapped to the corresponding part of the reference image by using an automated image registration algorithm. A normalized cross-correlation (NCC) function or mutual information was used as the auto-mapping metric and a limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS) was employed to optimize the function to find the optimal mapping. For rigid registration, the transformation parameters of the system are obtained by averaging that derived from the individual control volumes. In our deformable calculation, the mapped control volumes are treated as the nodes or control points with known positions on the two images. If the number of control volumes is not enough to cover the whole image to be registered, additional nodes are placed on the model image and then located on the reference image in a manner similar to the conventional BSpline deformable calculation. For deformable registration, the established correspondence by the auto-mapped control volumes provides valuable guidance for the registration calculation and greatly reduces the dimensionality of the problem. The performance of the two-step registrations was applied to three rigid registration cases (two PET-CT registrations and a brain MRI-CT registration) and one deformable registration of inhale and exhale phases of a lung 4D CT. Algorithm convergence was confirmed by starting the registration calculations from a large number of initial transformation parameters. An accuracy of approximately 2 mm was achieved for both deformable and rigid registration. The proposed image registration method greatly reduces the complexity involved in the determination of homologous control points and allows us to minimize the subjectivity and uncertainty associated with the current manual interactive approach. Patient studies have indicated that the two-step registration technique is fast, reliable, and provides a valuable tool to facilitate both rigid and nonrigid image registrations.     

Combination of intensity-based image registration with 3D simulation in radiation therapy

Modern techniques of radiotherapy like intensity modulated radiation therapy (IMRT) make it possible to deliver high dose to tumors of different irregular shapes at the same time sparing surrounding healthy tissue. However, internal tumor motion makes precise calculation of the delivered dose distribution challenging. This makes analysis of tumor motion necessary. One way to describe target motion is using image registration. Many registration methods have already been developed previously. However, most of them belong either to geometric approaches or to intensity approaches. Methods which take account of anatomical information and results of intensity matching can greatly improve the results of image registration. Based on this idea, a combined method of image registration followed by 3D modeling and simulation was introduced in this project. Experiments were carried out for five patients 4DCT lung datasets. In the 3D simulation, models obtained from images of end-exhalation were deformed to the state of end-inhalation. Diaphragm motions were around -25 mm in the cranial-caudal (CC) direction. To verify the quality of our new method, displacements of landmarks were calculated and compared with measurements in the CT images. Improvement of accuracy after simulations has been shown compared to the results obtained only by intensity-based image registration. The average improvement was 0.97 mm. The average Euclidean error of the combined method was around 3.77 mm. Unrealistic motions such as curl-shaped deformations in the results of image registration were corrected. The combined method required less than 30 min. Our method provides information about the deformation of the target volume, which we need for dose optimization and target definition in our planning system.     

Validation of an accelerated 'demons' algorithm for deformable image registration in radiation therapy

A greyscale-based fully automatic deformable image registration algorithm, originally known as the 'demons' algorithm, was implemented for CT image-guided radiotherapy. We accelerated the algorithm by introducing an 'active force' along with an adaptive force strength adjustment during the iterative process. These improvements led to a 40% speed improvement over the original algorithm and a high tolerance of large organ deformations. We used three methods to evaluate the accuracy of the algorithm. First, we created a set of mathematical transformations for a series of patient's CT images. This provides a 'ground truth' solution for quantitatively validating the deformable image registration algorithm. Second, we used a physically deformable pelvic phantom, which can measure deformed objects under different conditions. The results of these two tests allowed us to quantify the accuracy of the deformable registration. Validation results showed that more than 96% of the voxels were within 2 mm of their intended shifts for a prostate and a head-and-neck patient case. The mean errors and standard deviations were 0.5 mm+/-1.5 mm and 0.2 mm+/-0.6 mm, respectively. Using the deformable pelvis phantom, the result showed a tracking accuracy of better than 1.5 mm for 23 seeds implanted in a phantom prostate that was deformed by inflation of a rectal balloon. Third, physician-drawn contours outlining the tumour volumes and certain anatomical structures in the original CT images were deformed along with the CT images acquired during subsequent treatments or during a different respiratory phase for a lung cancer case. Visual inspection of the positions and shapes of these deformed contours agreed well with human judgment. Together, these results suggest that the accelerated demons algorithm has significant potential for delineating and tracking doses in targets and critical structures during CT-guided radiotherapy.     

亚像素断层图像配准数据集的建立

目的针对数字化冰冻铣切断层图像的特点,探讨一种实用的高精度图像配准方法,建立基于数字化断层图像的亚像素级配准数据集。方法采用冰冻铣切技术获取成年男性头颈标本的冰冻连续断层图像,在M atlab软件中自动提取定标点图像特征,采用基于2点的刚体变换算法实现图像的自动配准。结果配准后图像定标点与基准配准点的误差小于1个像素,达到亚像素水平。结论采用外定标的图像配准算法可建立亚像素级的配准数据集,定位标记物的准确识别是获得亚像素级配准数据集的保证。     

A universal algorithm for an improved finite element mesh generation Mesh quality assessment in comparison to former automated mesh-generators and an analytic model

The FE-modeling of complex anatomical structures is not solved satisfyingly so far. Voxel-based as opposed to contour-based algorithms allow an automated mesh generation based on the image data. Nonetheless their geometric precision is limited. We developed an automated mesh-generator that combines the advantages of voxel-based generation with improved representation of the geometry by displacement of nodes on the object-surface. Models of an artificial 3D-pipe-section and a skullbase were generated with different mesh-densities using the newly developed geometric, unsmoothed and smoothed voxel generators. Compared to the analytic calculation of the 3D-pipe-section model the normalized RMS error of the surface stress was 0.173-0.647 for the unsmoothed voxel models, 0.111-0.616 for the smoothed voxel models with small volume error and 0.126-0.273 for the geometric models. The highest element-energy error as a criterion for the mesh quality was 2.61x10(-2) N mm, 2.46x10(-2) N mm and 1.81x10(-2) N mm for unsmoothed, smoothed and geometric voxel models, respectively. The geometric model of the 3D-skullbase resulted in the lowest element-energy error and volume error. This algorithm also allowed the best representation of anatomical details. The presented geometric mesh-generator is universally applicable and allows an automated and accurate modeling by combining the advantages of the voxel-technique and of improved surface-modeling.     

Algorithms for radiological image registration and their clinical application

This paper reviews recent work in radiological image registration and provides a classification of image registration by type of transformation and by methods employed to compute the transformation. The former includes transformation of 2D images to 2D images of the same individual, transformation of 3D images to 3D images of the same individual, transformation of images to an atlas or model, transformation of images acquired from a number of individuals, transformations for image guided interventions including 2D to 3D registration and finally tissue deformation in image guided interventions. Recent work on computing transformations for registration using corresponding landmark based registration, surface based registration and voxel similarity measures, including entropy based measures, are reviewed and compared. Recently fully automated algorithms based on voxel similarity measures and, in particular, mutual information have been shown to be accurate and robust at registering images of the head when the rigid body assumption is valid. Two approaches to modelling soft tissue deformation for applications in image guided interventions are described. Validation of complex processing tasks such as image registration is vital if these algorithms are to be used in clinical practice. Three alternative validation strategies are presented. These methods are finding application outside the original domain of radiological imaging.     

Intensity based image registration by minimizing exponential function weighted residual complexity

In this paper, we propose a novel intensity-based similarity measure for medical image registration. Traditional intensity-based methods are sensitive to intensity distortions, contrast agent and noise. Although residual complexity can solve this problem in certain situations, relative modification of the parameter can generate dramatically different results. By introducing a specifically designed exponential weighting function to the residual term in residual complexity, the proposed similarity measure performed well due to automatically weighting the residual image between the reference image and the warped floating image. We utilized local variance of the reference image to model the exponential weighting function. The proposed technique was applied to brain magnetic resonance images, dynamic contrast enhanced magnetic resonance images (DCE-MRI) of breasts and contrast enhanced 3D CT liver images. The experimental results clearly indicated that the proposed approach has achieved more accurate and robust performance than mutual information, residual complexity and Jensen–Tsallis.     

利用相关比相似性测度多分辨率配准MR和PET医学图像的方法

采用了全新的相关比相似性测度作为配准的测度准则，提出了有效的磁共振(MR)和正电子发射端层扫描(PET)临床医学图像配准方法。具体设计时，采用了加速的多分辨率的配准方案，对方案中涉及的几何变换选取、重采样、多分辨率体数据表达及最优化方法进行了详细的设计分析。最后，利用多分辨率配准方法，对MR和PET临床医学图像进行配准，给出了令人满意的效果，同时和基于体素灰度的直接配准法相比，配准速度也有了很大提高。     

A second-order finite element algorithm for solving the three-dimensional EEG forward problem

A finite element algorithm has been developed to solve the electroencephalogram (EEG) forward problem. A new computationally efficient approach to calculate the stiffness matrix of second-order tetrahedral elements has been developed for second-order tetrahedral finite element models. The present algorithm has been evaluated by means of computer simulations, by comparing with analytic solutions in a multi-spheres concentric head model. The developed finite element method (FEM) algorithm has also been applied to address questions of interest in the EEG forward problem. The present simulation study indicates that the second-order FEM provides substantially enhanced numerical accuracy and computational efficiency, as compared with the first-order FEM for comparable numbers of tetrahedral elements. The anisotropic conductivity distribution of the head tissue can be taken into account in the present FEM algorithm. The effects of dipole eccentricity, size of finite elements and local mesh refinement on solution accuracy are also addressed in the present simulation study.