B-spline Algorithm Research Articles

Adaptive radiotherapy for NSCLC patients: utilizing the principle of energy conservation to evaluate dose mapping operations

Tumor regression during the course of fractionated radiotherapy confounds the ability to accurately estimate the total dose delivered to tumor targets. Here we present a new criterion to improve the accuracy of image intensity-based dose mapping operations for adaptive radiotherapy for patients with non-small cell lung cancer (NSCLC). Six NSCLC patients were retrospectively investigated in this study. An image intensity-based B-spline registration algorithm was used for deformable image registration (DIR) of weekly CBCT images to a reference image. The resultant displacement vector fields were employed to map the doses calculated on weekly images to the reference image. The concept of energy conservation was introduced as a criterion to evaluate the accuracy of the dose mapping operations. A finite element method (FEM)-based mechanical model was implemented to improve the performance of the B-Spline-based registration algorithm in regions involving tumor regression. For the six patients, deformed tumor volumes changed by 21.2 ± 15.0% and 4.1 ± 3.7% on average for the B-Spline and the FEM-based registrations performed from fraction 1 to fraction 21, respectively. The energy deposited in the gross tumor volume (GTV) was 0.66 Joules (J) per fraction on average. The energy derived from the fractional dose reconstructed by the B-spline and FEM-based DIR algorithms in the deformed GTV’s was 0.51 J and 0.64 J, respectively. Based on landmark comparisons for the 6 patients, mean error for the FEM-based DIR algorithm was 2.5 ± 1.9 mm. The cross-correlation coefficient between the landmark-measured displacement error and the loss of radiation energy was −0.16 for the FEM-based algorithm. To avoid uncertainties in measuring distorted landmarks, the B-Spline-based registrations were compared to the FEM registrations, and their displacement differences equal 4.2 ± 4.7 mm on average. The displacement differences were correlated to their relative loss of radiation energy with a cross-correlation coefficient equal to 0.68. Based on the principle of energy conservation, the FEM-based mechanical model has a better performance than the B-Spline-based DIR algorithm. It is recommended that the principle of energy conservation be incorporated into a comprehensive QA protocol for adaptive radiotherapy.

Prognostic factors associated with the accuracy of deformable image registration in lung cancer patients treated with stereotactic body radiotherapy

We evaluated the accuracy of an in-house program in lung stereotactic body radiation therapy (SBRT) cancer patients, and explored the prognostic factors associated with the accuracy of deformable image registrations (DIRs). The accuracy of the 3 programs which implement the free-form deformation and the B-spline algorithm was compared regarding the structures on 4-dimensional computed tomography (4DCT) image datasets between the peak-inhale and peak-exhale phases. The dice similarity coefficient (DSC) and normalized DSC (NDSC) were measured for the gross tumor volumes from 19 lung SBRT patients. We evaluated the accuracy of DIR using gross tumor volume, magnitude of displacement from 0% phase to 50% phase, whole lung volume in the 50% phase image, and status of tumor pleural attachment. The median NDSC values using the NiftyReg, MIM Maestro and Velocity AI programs were 1.027, 1.005, and 0.946, respectively, indicating that NiftyReg and MIM Maestro programs had similar accuracy with an uncertainty of < 1 mm. Larger uncertainty of 1 to 2 mm was observed using the Velocity AI program. The NiftyReg and the MIM programs provided higher NDSC values than the median values when the gross tumor volume was attached to the pleura (p < 0.05). However, it showed a different trend in using the Velocity AI program. All software programs provided unexpected results, and there is a possibility that such results would reduce the accuracy of 4D treatment planning and adaptive radiotherapy. The unexpected results may be because the tumors are surrounded by other tissues, and there are differences regarding the region of interest for rigid and nonrigid registration. Furthermore, our results indicated that the pleural attachment status might be an important predictor of DIR accuracy for thoracic images, indicating that there is a potentially large dose distribution discrepancy concerning 4D treatment planning and adaptive radiotherapy.

Extended modified cubic B-spline algorithm for nonlinear Burgers' equation

In this paper, an extended modified cubic B-Spline differential quadrature method is proposed to approximate the solution of the nonlinear Burgers' equation. The proposed method is used in space and a five-stage and four order strong stability-preserving time-stepping Runge–Kutta (SSP-RK54) method is used in time. The accuracy and efficiency of the method is illustrated by considering four numerical problems. The numerical results of the method are compared with some existing methods and it was found that the proposed numerical method produces acceptable results and even more accurate results in comparison with some existing methods. The stability analysis of the scheme is also carried out and was found to be unconditionally stable.

Effects of Resolution and Registration Algorithm on the Accuracy of EPI vNavs for Real Time Head Motion Correction in MRI.

Low-resolution, EPI-based Volumetric Navigators (vNavs) have been used as a prospective motion-correction system in a variety of MRI neuroimaging pulse sequences. The use of low-resolution volumes represents a trade-off between motion tracking accuracy and acquisition time. However, this means that registration must be accurate on the order of 0.2 voxels or less to be effective for motion correction. While vNavs have shown promising results in clinical and research use, the choice of navigator and registration algorithm have not previously been systematically evaluated. In this work we experimentally evaluate the accuracy of vNavs, and possible design choices for future improvements to the system, using real human data. We acquired navigator volumes at three isotropic resolutions (6.4 mm, 8 mm, and 10 mm) with known rotations and translations. The vNavs were then rigidly registered using trilinear, tricubic, and cubic B-spline interpolation. We demonstrate a novel refactoring of the cubic B-spline algorithm that stores pre-computed coefficients to reduce the per-interpolation time to be identical to tricubic interpolation. Our results show that increasing vNav resolution improves registration accuracy, and that cubic B-splines provide the highest registration accuracy at all vNav resolutions. Our results also suggest that the time required by vNavs may be reduced by imaging at 10 mm resolution, without substantial cost in registration accuracy.

SU‐F‐J‐80: Deformable Image Registration for Residual Organ Motion Estimation in Respiratory Gated Treatments with Scanned Carbon Ion Beams

Purpose:At the Centro Nazionale di Adroterapia Oncologica (CNAO, Pavia, Italy) C‐ions respiratory gated treatments of patients with abdominal tumours started in 2014. In these cases, the therapeutic dose is delivered around end‐exhale. We propose the use of a respiratory motion model to evaluate residual tumour motion. Such a model requires motion fields obtained from deformable image registration (DIR) between 4DCT phases, estimating anatomical motion through interpolation. The aim of this work is to identify the optimal DIR technique to be integrated in the modeling pipeline.Methods:We used 4DCT datasets from 4 patients to test 4 DIR algorithms: Bspline, demons, log‐domain and symmetric log domain diffeomorphic demons. We evaluate DIR performance in terms of registration accuracy (RMSE between registered images) and anatomical consistency of the motion field (Jacobian) when registering end‐inhale to end‐exhale. We subsequently employed the model to estimate the tumour trajectory within the ideal gating window.Results:Within the liver contour, the RMSE is in the range 31–46 HU for the best performing algorithm (Bspline) and 43–145 HU for the worst one (demons). The Jacobians featured zero negative voxels (which indicate singularities in the motion field) for the Bspline fields in 3 of 4 patients, whereas diffeomorphic demons fields showed a non‐null number of negative voxels in every case. GTV motion in the gating window measured less than 7 mm for every patient, displaying a predominant superior‐inferior (SI) component.Conclusion:The Bspline algorithm allows for acceptable DIR results in the abdominal region, exhibiting the property of anatomical consistency of the computed field. Computed trajectories are in agreement with clinical expectations (small and prevalent SI displacements), since patients lie wearing semi‐rigid immobilizing masks. In future, the model could be used for retrospective estimation of organ motion during treatment, as guided by the breathing surrogate signal.

Measuring and presetting system for tool electrodes used for machining rimmed turbine blisks

The aim of the study is to develop a measuring and presetting system for tool electrodes used for machining rimmed turbine blisks. A data-sampling method based on voltage monitoring was established as the foundation of this study. The proposed system, which consisted of three parts (mechanical, electric control and computer numerical control system software), was then realized. The method for extracting characteristic points from the theoretical model of the tool electrode and the bicubic B-spline algorithms for reconstructing the actual model of the tool electrode were established. A simulation analysis of the surface deviation was conducted to verify the extracting method and the algorithms. Next, a suitable accuracy evaluation method was developed to evaluate the accuracy of the tool electrode. Several experiments were performed to verify the performance of the system. Currently, the system is applied to practical production and has shown satisfactory results.

Human Detection Framework for Automated Surveillance Systems

Vision-based systems for surveillance applications have been used widely and gained more research attention. Detecting people in an image stream is challenging because of their intra-class variability, the diversity of the backgrounds, and the conditions under which the images were acquired. Existing human detection solutions suffer in their effectiveness and efficiency. In particular, the accuracy of the existing detectors is characterized by their high false positive and negative. In addition, existing detectors are slow for online surveillance systems which lead to large delay that is not suitable for surveillance systems for real-time monitoring. In this paper, a holistic framework is proposed for enhancing the performance of human detection in surveillance system. In general, the framework includes the following stages: environment modeling, motion object detection, and human object recognition. In environment modeling, modal algorithm has been suggested for background initialization and extraction. Then for effectively classifying the motion object, edge detecting and B-spline algorithm have been used for shadow detection and removal. Then, enhanced Lucas–Kanade optical flow has been used to get the area of interest for object segmentation. Finally, to enhance the segmentation, some morphological processes were performed. In the motion object recognition stage, segmentation for each blob is performed and processed to the human detector which is a complete learning-based system for detecting and localizing objects/humans in images using mixtures of deformable part models (PFF detector). Results show enhancement in each phase of the proposed framework. These enhancements are shown in the overall performance of human detection in surveillance system.

The exponential cubic B-spline algorithm for Fisher equation

In this study, exponential B-spline collocation method is set up for solving Fisher’s equation. Integration of Fisher’s equation is managed by use of the exponential cubic B-spline in space and the Crank–Nicolson method in time. The effect of reaction and diffusion is observed by studying three test problems. A comparison is performed between the obtained numerical results and some earlier results using L∞ and relative error norms.

A Subdivision Based Iterative Collocation Algorithm for Nonlinear Third-Order Boundary Value Problems

We construct an algorithm for the numerical solution of nonlinear third-order boundary value problems. This algorithm is based on eight-point binary subdivision scheme. Proposed algorithm is stable and convergent and gives more accurate results than fourth-degree B-spline algorithm.

Characterization of deformation and physical force in uniform low contrast anatomy and its impact on accuracy of deformable image registration.

Little is known about the effect of force on organ deformation and consequently its impact on precision dose delivery. The purpose of this study was to evaluate the fundamental relationship between anatomic deformation and its causative physical force to ascertain if a threshold limit exists for deformable image registration (DIR) accuracy in uniform low contrast anatomy, beyond which its applicability may be clinically inappropriate. To simulate a simplified model, a tissue equivalent deformable bladder phantom with 21 implanted fiducial markers was developed using a viscoelastic polymer. The bladder phantom was deformed by applying a force in increments from 10 to 70 N. DIR accuracy was studied using intensity based mim and Velocity B-spline algorithms by comparing the 3D vector of the 21 marker locations at the original target image with the synthetically derived marker positions from each target image obtained from DIR. The relationship between applied force in 1D deformation along the axis of applied force and 3D deformation of the phantom showed a linear response. The maximum and average displacements of markers exhibited a nonlinear response to the applied force. In the absence of implanted markers, DIR performance was suboptimal with a threshold limit of only 20 N (5 mm deformation) beyond which the average marker error was ≥3 mm. DIR performance improved significantly with the addition of only one marker for the intensity based mim algorithm. In contrast, the Velocity B-spline algorithm showed reduced sensitivity to the number of markers introduced in both the source and target images. The limits of applicability of DIR are strongly dependent on the magnitude of deformation. There is a threshold limit beyond which the accuracy of DIR fails in uniform low contrast anatomy. The sensitivity of the DIR performance to the number of fiducial markers present indicates that if DIR performance is solely assessed with the contrast rich features present in clinical anatomy, the results may not be reflective of the true DIR performance in uniform low contrast anatomy.

Abstract A88: Voxel-based tracking of 18F-FDG PET images for evaluation of treatment response for NSCLC patients

Abstract Purpose: To improve the accuracy of tumor response assessed using 18F-Fluorodeoxyglucose Position Emission Tomography (18F-FDG PET), a new deformable image registration technique was investigated that has potential to more precisely track changes of the standardized uptake value (SUV) at each image voxel. FDG-PET/CT is a standard clinical tool for cancer detection and the assessment of tumor response to treatment. However, due to the lack of anatomical information in the PET images, a point-by-point assessment of treatment response cannot be derived directly from successive PET images until their associated CT images are appropriately registered. Due to tumor reduction following therapy, the conventional image intensity-based deformable image registration algorithms will shrink the tumor volume to match the residual target, but this could cause the responses evaluated from the two PET images mismatched. We propose an improved deformable image registration technique and demonstrate its potential to evaluate tumor response to radiation in lung cancer patients. Methods: An IMRT treatment plan was developed in a Pinnacle system with contours delineated on a 4DCT image. 18F-FDG PET images were acquired before and after treatment. The 4DCT was rigidly aligned to the pre-treatment PET-CT image. Peak activities normalized to the mean intravascular background in the aortic arch were used to determine relative SUV values. The PET images were refined to the same resolution as the associated CT images using a bilinear interpolation. The two PET-CT images were registered initially with an intensity-based B-spline algorithm implemented in the VelocityAI software, and then with an in-house developed adaptive finite element method (FEM) that used a bounding box of the residual tumor volume defined in the pre-treatment PET-CT image. The bounding box was partitioned into a tetrahedral mesh with the boundary constraints assigned from the VelocityAI generated displacement vector field (DVF). The resultant FEM displacements were used to adjust the VelocityAI registration within the box. The pre-treatment PET image was warped to the post-treatment PET using the two DVFs. The relative SUV differences between the warped and post-treatment PET images were counted as the treatment response. The CT images warped by the two registrations were visually inspected, and the constancy of the warped gross tumor volume (GTVCT) between the pre- and post-treatment CT images was taken as an evaluation criterion. The displacement differences between the two registration methods were calculated and their consequences in the warped PET images were evaluated. Results: With the DVFs generated by the VelocityAI and FEM registrations, the warped GTVCT volumes were reduced 32.8% and 5.7%, respectively. The mean displacement difference between the two registrations is 3.8 mm within the bounding box. The relative SUV was reduced to 12.8% in GTVCT after the completion of the treatment, and the averages of the SUV values mapped by the two DVFs are 3.6 and 4.1. Conclusions: The adaptive image registration method developed was used to correct anatomical deformation. The method can preserve peak activities and relative SUVs after registration of regressed tumors, and therefore could be used for tracking SUV changes in the follow-up PET images. Citation Format: Hualiang Zhong, Stephen Brown, Indrin J. Chetty. Voxel-based tracking of 18F-FDG PET images for evaluation of treatment response for NSCLC patients. [abstract]. In: Proceedings of the AACR-NCI-EORTC International Conference: Molecular Targets and Cancer Therapeutics; 2015 Nov 5-9; Boston, MA. Philadelphia (PA): AACR; Mol Cancer Ther 2015;14(12 Suppl 2):Abstract nr A88.

Four Dimensional Magnetic Resonance Imaging With 3D Radial Sampling and Self-gating Based K-space Sorting: Early Clinical Experience on Pancreatic Cancer Patients

Dynamic magnetic resonance imaging (MRI) has been used to characterize internal organ motion, but real-time acquisition has been limited to 2 dimensions (2D). Methods have been developed to reconstruct four dimensional MRI (4D-MRI) based on rebinning time-stamped 2D images or 2D K-space data. These methods suffer from anisotropic resolution and rebinning artifacts. We developed a 4D-MRI technique using 3D radial sampling and self-gating based K-space sorting (SG-KS-4D-MRI) to overcome these limitations, and applied it to study the target motion of pancreatic cancer patients. Ten patients were imaged during free breathing using 4D-CT, cine 2D-MRI and the SG-KS-4D-MRI method, which is an 8-minute spoiled gradient recalled echo (GRE) sequence with 3D radial-sampling K-space projections and 1D projection based self-gating. Tumor volumes were drawn at the end of exhalation phases in the SG-KS-4D-MRI and 4D-CT for each patient, and then mapped to the other phases using deformable registration with B-spline algorithm. Tumor volumes and motion trajectories were compared. An isotropic resolution of 1.6 mm was achieved in the SG-KS-4D-MRI images, which showed superior soft tissue contrast to 4D-CT and were free of visible rebinning artifacts. The tumor motion trajectory cross-correlations between SG-KS-4D-MRI and cine 2D-MRI directions in superior-inferior (SI), anterior-posterior (AP) and medial-lateral (ML) directions were 0.93 ± 0.03, 0.83 ± 0.10, and 0.74 ± 0.18, respectively. The tumor motion trajectory cross-correlations between the SG-KS-4D-MRI and 4D-CT in SI, AP and ML were 0.91 ± 0.06, 0.72 ± 0.18, and 0.44 ± 0.24, respectively. The average motion amplitude differences (Ddiff) between SG-KS-4D-MRI and cine 2D-MRI in SI, AP, and ML directions were 0.83 ± 0.52, 0.40 ± 0.17, and 0.48 ± 0.24 mm. The Ddiff between SG-KS-4D-MRI and 4D-CT in SI, AP, and ML directions were 1.09 ± 0.43, 0.53 ± 0.24, and 0.47 ± 0.26 mm, respectively. The average standard deviations of the GTV volumes (GTV_σ) calculated from each of the ten breathing phases were 0.8 cm3 (SG-KS-4D-MRI) and 1.0 cm3 (4D-CT), P = .004, indicating a statistically significant difference between the two imaging modalities. A novel 4D-MRI imaging sequence, SG-KS-4D-MRI, was used to evaluate target motion for free breathing pancreatic cancer patients. Pancreatic motion trajectories agreed well with 4D-CT and cine 2D-MRI data in the SI and AP directions, but agreement was limited in the ML direction, where image pixel size and displacements are of similar size. Use of SG-KS-4D-MRI results in improved spatial resolution, voxel isotropy, and gives an average motion pattern over an extended period of time; SG-KS-4D-MRI also results in statistically more consistent tumor volume definition across the ten breathing phases.

SU-E-J-109: Evaluation of Deformable Accumulated Parotid Doses Using Different Registration Algorithms in Adaptive Head and Neck Radiotherapy

Purpose: Three deformable image registration (DIR) algorithms are utilized to perform deformable dose accumulation for head and neck tomotherapy treatment, and the differences of the accumulated doses are evaluated. Methods: Daily MVCT data for 10 patients with pathologically proven nasopharyngeal cancers were analyzed. The data were acquired using tomotherapy (TomoTherapy, Accuray) at the PLA General Hospital. The prescription dose to the primary target was 70Gy in 33 fractions.Three DIR methods (B-spline, Diffeomorphic Demons and MIMvista) were used to propagate parotid structures from planning CTs to the daily CTs and accumulate fractionated dose on the planning CTs. The mean accumulated doses of parotids were quantitatively compared and the uncertainties of the propagated parotid contours were evaluated using Dice similarity index (DSI). Results: The planned mean dose of the ipsilateral parotids (32.42±3.13Gy) was slightly higher than those of the contralateral parotids (31.38±3.19Gy)in 10 patients. The difference between the accumulated mean doses of the ipsilateral parotids in the B-spline, Demons and MIMvista deformation algorithms (36.40±5.78Gy, 34.08±6.72Gy and 33.72±2.63Gy ) were statistically significant (B-spline vs Demons, P<0.0001, B-spline vs MIMvista, p =0.002). And The difference between those of the contralateral parotids in the B-spline, Demons and MIMvista deformation algorithms (34.08±4.82Gy, 32.42±4.80Gy and 33.92±4.65Gy ) were also significant (B-spline vs Demons, p =0.009, B-spline vs MIMvista, p =0.074). For the DSI analysis, the scores of B-spline, Demons and MIMvista DIRs were 0.90, 0.89 and 0.76. Conclusion: Shrinkage of parotid volumes results in the dose increase to the parotid glands in adaptive head and neck radiotherapy. The accumulated doses of parotids show significant difference using the different DIR algorithms between kVCT and MVCT. Therefore, the volume-based criterion (i.e. DSI) as a quantitative evaluation of registration accuracy is essential besides the visual assessment by the treating physician. This work was supported in part by the grant from Chinese Natural Science Foundation (Grant No. 11105225).

SU-E-J-107: The Impact of the Tumor Location to Deformable Image Registration

Purpose: For four-dimensional planning and adaptive radiotherapy, the accuracy of deformable image registration (DIR) is essential. We evaluated the accuracy of an in-house program with the free-downloadable DIR software library package (NiftyReg) and two commercially available DIR software programs (MIM Maestro and Velocity AI) in lung SBRT cancer patients. In addition to it, the relationship between the tumor location and the accuracy of the DIRs was investigated. Methods: The free-form deformation was implemented in the in-house program and the MIM. The Velocity was based on the B-spline algorithm. The accuracy of the three programs was evaluated in comparison for the structures on 4DCT image datasets between at the peak-inhale and at the peak-exhale. The dice similarity coefficient (DSC) and normalized DSC (NDSC) were measured for the gross tumor volumes from 19 lung SBRT patients. Results: The DSC measurement showed the median values of the DSC were 0.885, 0.872 and 0.798 for the In-house program, the MIM and the Velocity, respectively. The Velocity showed significant difference compared to the others. The median NDSC values were 1.027, 1.005 and 0.946 for the In-house, the MIM and the Velocity, respectively. This indicated that the spatial overlap agreement between the reference and the deformed structure for the in-house and MIM was comparable with the accuracy within 1mm uncertainty. There was larger discrepancy within 1–2mm uncertainty for the Velocity. The In-house and the MIM showed the higher NDSC values than the median values when the GTV was not attached to the chest wall and diaphragm(p < 0.05). However, there is no relationship between the accuracy and the tumor location in the Velocity. Conclusion: The difference of the DIR program would affect different accuracy and the accuracy may be reduced when the tumor is located or attached to chest wall or diaphragm.

Two Dimensional Intelligent Feedrate Control Incorporating Stage Dynamics

This paper studies the dynamic feedrate control problem for mechanical stages performing contouring actions. In modern researches, feedrate is considered as a dynamic factor instead of simple constant value in the traditional methods, and should be properly controlled to meet higher precision standard nowadays. To incorporate the dynamic feedrate in the path interpolation, the so called non-uniform rational B-spline (NURBS) algorithm is utilized to form the fundamental real-time interpolation structure of this research. The result of a sophisticated intelligent feedrate control design is then proposed where the system feedrate is real-time determined based on both the feedback of the path curvature and the measured contour error. Experiments and comparative studies for free-form paths are also conducted where the results show that the proposed design indeed can provide significant precision improvement in overall contouring performance in contrast to the traditional method. Therefore, the effectiveness and the goal of the proposed method can be verified which suggests that the entire scheme has the potential for real industrial applications.

Deformable image registration based on elastodynamics

This paper presents a novel method for 2D inter-subject non-rigid image registration. It is motivated by the ideas derived from elastodynamics which is the subclass of linear elastic theory. We propose to model the non-rigid deformations as elastic waves which are characterized by elastodynamics wave equation. Our registration method is formulated in a multi-resolution manner such that it is able to recover significant deformations. The proposed scheme recovers local (non-linear) as well as global deformations. The results of image registration by the proposed technique were validated via similarity measures for real MR brain images, BrainWeb dataset and MR prostate images. We have also used overlap measures (Jaccard distance, Dice coefficient and Overlap coefficient) over the segmented deep-brain structures including: lateral and third ventricles, putamen and caudate nucleus for real image dataset to further validate our proposed registration scheme. The proposed scheme was also compared with demons, Level set and free-form deformations (cubic B-spline) algorithms implemented in ITK toolkit and symmetric normalization method available in ANTs software package. Our proposed algorithm shows marked improvement of the inter-subject non-rigid registration, both qualitatively and quantitatively, over the four above-mentioned methods. This comparison was performed on all the three types of datasets mentioned above. 2D synthetic experiments comprising of Patch-`C', Square---Rectangle and Circle-`C' were also performed with our algorithm and compared with other four methods. Both qualitative and quantitative results show that our method performs better than the other four methods. Results suggest that our proposed algorithm has improved accuracy over lemons, level set and free-form deformations (ITK implemented) and symmetric normalization method (ANTs based), tested over two types of brain and one prostate MRI. The commonly used synthetic experiments also suggest the superiority of our proposed scheme.

A hybrid biomechanical intensity based deformable image registration of lung 4DCT

Deformable image registration (DIR) has been extensively studied over the past two decades due to its essential role in many image-guided interventions (IGI). IGI demands a highly accurate registration that maintains its accuracy across the entire region of interest. This work evaluates the improvement in accuracy and consistency by refining the results of Morfeus, a biomechanical model-based DIR algorithm.A hybrid DIR algorithm is proposed based on, a biomechanical model–based DIR algorithm and a refinement step based on a B-spline intensity-based algorithm. Inhale and exhale reconstructions of four-dimensional computed tomography (4DCT) lung images from 31 patients were initially registered using the biomechanical DIR by modeling contact surface between the lungs and the chest cavity. The resulting deformations were then refined using the intensity-based algorithm to reduce any residual uncertainties. Important parameters in the intensity-based algorithm, including grid spacing, number of pyramids, and regularization coefficient, were optimized on 10 randomly-chosen patients (out of 31). Target registration error (TRE) was calculated by measuring the Euclidean distance of common anatomical points on both images after registration. For each patient a minimum of 30 points/lung were used.Grid spacing of 8 mm, 5 levels of grid pyramids, and regularization coefficient of 3.0 were found to provide optimal results on 10 randomly chosen patients. Overall the entire patient population (n = 31), the hybrid method resulted in mean ± SD (90th%) TRE of 1.5 ± 1.4 (2.9) mm compared to 3.1 ± 1.9 (5.6) using biomechanical DIR and 2.6 ± 2.5 (6.1) using intensity-based DIR alone.The proposed hybrid biomechanical modeling intensity based algorithm is a promising DIR technique which could be used in various IGI procedures. The current investigation shows the efficacy of this approach for the registration of 4DCT images of the lungs with average accuracy of 1.5 mm.

The Exponential Cubic B-Spline Algorithm for Korteweg-de Vries Equation

The exponential cubic B-spline algorithm is presented to find the numerical solutions of the Korteweg-de Vries (KdV) equation. The problem is reduced to a system of algebraic equations, which is solved by using a variant of Thomas algorithm. Numerical experiments are carried out to demonstrate the efficiency of the suggested algorithm.

Validation of a deformable image registration technique for cone beam CT-based dose verification.

As radiation therapy evolves toward more adaptive techniques, image guidance plays an increasingly important role, not only in patient setup but also in monitoring the delivered dose and adapting the treatment to patient changes. This study aimed to validate a method for evaluation of delivered intensity modulated radiotherapy (IMRT) dose based on multimodal deformable image registration (dir) for prostate treatments. A pelvic phantom was scanned with CT and cone-beam computed tomography (CBCT). Both images were digitally deformed using two realistic patient-based deformation fields. The original CT was then registered to the deformed CBCT resulting in a secondary deformed CT. The registration quality was assessed as the ability of the dir method to recover the artificially induced deformations. The primary and secondary deformed CT images as well as vector fields were compared to evaluate the efficacy of the registration method and it's suitability to be used for dose calculation. plastimatch, a free and open source software was used for deformable image registration. A B-spline algorithm with optimized parameters was used to achieve the best registration quality. Geometric image evaluation was performed through voxel-based Hounsfield unit (HU) and vector field comparison. For dosimetric evaluation, IMRT treatment plans were created and optimized on the original CT image and recomputed on the two warped images to be compared. The dose volume histograms were compared for the warped structures that were identical in both warped images. This procedure was repeated for the phantom with full, half full, and empty bladder. The results indicated mean HU differences of up to 120 between registered and ground-truth deformed CT images. However, when the CBCT intensities were calibrated using a region of interest (ROI)-based calibration curve, these differences were reduced by up to 60%. Similarly, the mean differences in average vector field lengths decreased from 10.1 to 2.5 mm when CBCT was calibrated prior to registration. The results showed no dependence on the level of bladder filling. In comparison with the dose calculated on the primary deformed CT, differences in mean dose averaged over all organs were 0.2% and 3.9% for dose calculated on the secondary deformed CT with and without CBCT calibration, respectively, and 0.5% for dose calculated directly on the calibrated CBCT, for the full-bladder scenario. Gamma analysis for the distance to agreement of 2 mm and 2% of prescribed dose indicated a pass rate of 100% for both cases involving calibrated CBCT and on average 86% without CBCT calibration. Using deformable registration on the planning CT images to evaluate the IMRT dose based on daily CBCTs was found feasible. The proposed method will provide an accurate dose distribution using planning CT and pretreatment CBCT data, avoiding the additional uncertainties introduced by CBCT inhomogeneity and artifacts. This is a necessary initial step toward future image-guided adaptive radiotherapy of the prostate.

The Benefits of Bezier, B-Spline Algorithm in the Industry World

Computer Graphics is a science which is widely used in all fields, especially in the fied of Industries, companies, banking and even hospitals. In the aviation industries, marines and automotves, computer graphics with its latest technologies, can be used to solve graphical or imaging problems. Wherever images is involved, for eaxmple for patients’ need in the hospitals, shipping engineers/designers or decision makers in an industry, the images can be analyzed in order to produce a better image in which the accuracy being continuously being researched. (CAD or CAM) (Newman and Sproull, 1981; Date, 1990; Pressman, 2001). The objective of this research is to combine the algorithms in order to create an image which is accurate and can be used by decision makers accordingly. This is performed by associating the Hermite, Bezier, B-Spline algorithms to its harmonic functions such that the resulting curves/images becomes better and more well-formed. This research will produce a picture/image/shape that will serve the needs of the designers. (Newman and Sproull, 1981; Connolly and Begg, 2002; Ramez et al., 2000; Date, 1990; Pressman, 2001).