Deformation Matrices Research Articles

Subject-Specific Probability Maps of Scalp, Skull and Cerebrospinal Fluid for Cranial Bones Segmentation in Neonatal Cerebral MRIs

ObjectivesSegmentation of cranial bones in magnetic resonance images (MRIs) is a challenging and indispensable task to study neonatal brain development and injury. This paper presents a new approach for creating subject-specific probability maps of the scalp, skull and cerebrospinal fluid (CSF) from retrospective bimodal (MR and CT) images acquired from neonates in the gestational age range of 39 to 42 weeks. These maps are subsequently employed for the segmentation of cranial bones in cerebral MRIs from neonates in the same age range. Material and methodsRetrospective MR and CT of neonates with normal head in the gestational age range of 39-42 weeks were preprocessed, segmented semi-automatically and employed as atlas data. For an input MR image acquired from a subject under study, a preprocessing stage and three main processing blocks were performed: First, subject-specific head and intracranial templates and CSF probability map were created using retrospective MR atlas data. Second, the CT atlas data were coregistered to MR templates and the resulted deformation matrices were fed to the next block to create subject-specific scalp and skull probability maps. Finally, some novel performance measures were presented to evaluate the performance of subject-specific CSF, scalp and skull probability maps for skull and intracranial segmentation in neonatal MRIs. ResultsThe subject-specific probability maps were employed for brain tissue extraction and compared with two public methods such as Brain Extraction Tool (BET) and Brain Surface Extractor (BSE). They were also applied for cranial bone extraction. Then, the similarity in shape between the frontal and occipital sutures (which had been reconstructed from segmented cranial bones) and the ground truth landmarks was evaluated. For this purpose, modified versions of the Dice similarity coefficient (DSC) were used. Finally, a retrospective bimodal (MR-CT) data acquired from a neonate within a short time interval was used for evaluation. After co-alignment of the two images, the DSC and modified Hausdorff distance (MHD) were used to compare the similarity of cranial bones in the MR and CT images. ConclusionSignificant improvements were achieved compared to conventional methods which rely solely on MR image intensities. These advancements hold promise for enhancing neurodevelopmental studies in neonates. The algorithm for creating subject-specific atlases is publicly accessible through a graphical user interface at medvispy.ee.kntu.ac.ir.

Результаты исследования матриц деформаций координатной основы СК-42

For transition from the coordinate system CS-42 to the Earth-centered, Earth-fixed SCS-2011, correct transformation models are required. Such a model is a non-linear transformation of coordinate systems via the grid shift method. The Data Grid of transformation parameters from CS-42, CS-95 to SCS-2011 were developed in 2016 at the Federal Scientific and Technical Center of Geodesy, Cartography and Spatial Data Infrastructure and are called deformation matrices of CS-95 (CS-42). The accuracy of coordinate transformation is declared as 10 cm for areas with a high density of state geodetic network points. The author presents the results of the deformation matrix analysis for the Republic of Bashkortostan. Evaluation of errors in it due to violation of the mesh irregularity is presented. Recommendations for improving the model are given

An accurate registration of the BigBrain dataset with the MNI PD25 and ICBM152 atlases

Brain atlases that encompass detailed anatomical or physiological features are instrumental in the research and surgical planning of various neurological conditions. Magnetic resonance imaging (MRI) has played important roles in neuro-image analysis while histological data remain crucial as a gold standard to guide and validate such analyses. With cellular-scale resolution, the BigBrain atlas offers 3D histology of a complete human brain, and is highly valuable to the research and clinical community. To bridge the insights at macro- and micro-levels, accurate mapping of BigBrain and established MRI brain atlases is necessary, but the existing registration is unsatisfactory. The described dataset includes co-registration of the BigBrain atlas to the MNI PD25 atlas and the ICBM152 2009b atlases (symmetric and asymmetric versions) in addition to manual segmentation of the basal ganglia, red nucleus, amygdala, and hippocampus for all mentioned atlases. The dataset intends to provide a bridge between insights from histological data and MRI studies in research and neurosurgical planning. The registered atlases, anatomical segmentations, and deformation matrices are available at: https://osf.io/xkqb3/.

Evaluation of Intensity- and Contour-Based Deformable Image Registration Accuracy in Pancreatic Cancer Patients.

We aimed to clarify the accuracy of rigid image registration and deformable image registration (DIR) in carbon-ion radiotherapy (CIRT) for pancreatic cancer. Six patients with pancreatic cancer who were treated with passive irradiation CIRT were enrolled. Three registration patterns were evaluated: treatment planning computed tomography images (TPCT) to CT images acquired in the treatment room (IRCT) in the supine position, TPCT to IRCT in the prone position, and TPCT in the supine position to the prone position. After warping the contours of the original CT images to the destination CT images using deformation matrices from the registration, the warped delineated contours on the destination CT images were compared with the original ones using mean displacement to agreement (MDA). Four contours (clinical target volume (CTV), gross tumor volume (GTV), stomach, duodenum) and four registration algorithms (rigid image registration [RIR], intensity-based DIR [iDIR], contour-based DIR [cDIR], and a hybrid iDIR-cDIR ([hDIR]) were evaluated. The means ± standard deviation of the MDAs of all contours for RIR, iDIR, cDIR, and hDIR were 3.40 ± 3.30, 2.2 1± 2.48, 1.46 ± 1.49, and 1.46 ± 1.37 mm, respectively. There were significant differences between RIR and iDIR, and between RIR/iDIR and cDIR/hDIR. For the pancreatic cancer patient images, cDIR and hDIR had better accuracy than RIR and iDIR.

Nonlinear elastic behavior and anisotropic electronic properties of two-dimensional borophene

Using first-principles density functional theory calculations, the mechanical and electronic properties of the three main (β12, χ3, and striped) phases of single-layer borophene sheets are calculated under in-plane uniaxial/biaxial strain, including the harmonic strain-energy regions of β12, χ3, and striped phases over the strain ranges of −3.5%–3.5%, −4.5%–4.5%, and −2.5%–2.5%, respectively, along the x direction (the direction of the highest bond orientation). We introduce a method by which the nonlinear behavior of these and any other two-dimensional materials can be investigated even above their ultimate strains, beyond which no-uniform plastic deformation occurs. Defining an appropriate deformation, and utilizing both continuum modeling and special equations based on the density functional theory, a method of computing second-, third-, and fourth-order elastic constants of the three different phases of borophene is presented that utilizes rectangular unit cells, which can substitute for any two-dimensional unit cell. Using this new method, 4 independent second-order, 6 third-order, and 9 fourth-order elastic constants are calculated, which is the complete set of elastic constants for two-dimensional structures. The electronic band structure of borophene shows anisotropic electronic behavior. Despite the metallic character of borophene sheets, applying directional strain based on deformation matrices creates a bandgap in some regions of the Brillouin zones, opening up the possibility of mechanical control of electronic properties.

Study of mechanical and electronic properties of single-layer FeB2

Recent experimental advances for the fabrication of various two dimensional (2D) materials introduced new structures with a wide prospect of applications. In this work, under in-plane uniaxial and biaxial strain, we employed first-principles density functional theory calculations to investigate the mechanical and electronic properties of Hexagonal Iron dibromide (FeB2) sheet. In mechanical section, we investigate deeply the mechanical analyzing of 2D structures to study elastic constants. Based on the results of our modelling, single layer FeB2 depending on the strain direction can yield remarkable elastic modulus in the range of 141.18 N/m for Young's modulus and also hold on ultimate stress up to 7.08 × 10−4 N/m, 7.96 × 10−4 N/m and 8.82 × 10−4 N/m at the corresponding strains 26.5%, 34% and 19.5% for uniaxial strain along x, y and biaxial strain, respectively. In this paper, second, third and fourth orders of elastic constants beside Young, Bulk and Shear's moduli and Poisson ratio of single layer of FeB2 have been determined, for the first time. By analyzing electronic band structure, we did not observe any band gaps in terms of strains. However, applying directional strain based on deformation matrices, bands get apart from Fermi level so that Dirac point has been vanished.

Mechanical and electronic properties of single-layer TiN and AlN under strain

Recent experimental advances for the fabrication of various two dimensional materials introduced new structures with a wide prospect of applications. In this work, under in-plane uniaxial/biaxial strain, we employed first-principles density functional theory calculations to investigate the mechanical and electronic properties of Aluminum Nitride (AlN) and Titanium Nitride (TiN) sheets. In mechanical section, we obtained second order elastic constants based on directional deformation applied on the structures. Based on the results of our modelling, TiN and AlN layers depending on the atomic configurations and the strain direction can yield remarkable elastic modulus in the range of 137.64 GPa nm for Young's module and high ultimate tensile strength from 6.29 N/m to around 18.34 N/m. In electronic section, by analyzing electronic band structure we observed the band gap variation in terms of strains, especially for AlN. It has 2.93 eV band gap in equilibrium condition, while shows 3.22 eV gap at −8% of uniaxial strain along x direction as the highest amount of originated gap. Despite metallic character of TiN, applying directional strain based on deformation matrices, creates a band gap in specific region of Brillouin zone.

Integrable flows between exact CFTs

We explicitly construct families of integrable σ-model actions smoothly inter-polating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels k1 and k2. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels k1 and k2 − k1. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.

Ventilation Series Similarity: A Study for Ventilation Calculation Using Deformable Image Registration and 4DCT to Avoid Motion Artifacts.

The major problem with ventilation distribution calculations using DIR and 4DCT is the motion artifacts in 4DCT. Quite often not all phases would exhibit mushroom motion artifacts. If the ventilation series similarity is sufficiently robust, the ventilation distribution can be calculated using only the artifact-free phases. This study investigated the ventilation similarity among the data derived from different respiration phases. Fifteen lung cancer cases were analyzed. In each case, DIR was performed between the end-expiration phase and all other phases. Ventilation distributions were then calculated using the deformation matrices. The similarity was compared between the series ventilation distributions. The correlation between the majority phases was reasonably good, with average SCC values between 0.28 and 0.70 for the original data and 0.30 and 0.75 after smoothing. The better correlation between the neighboring phases, with average SCC values between 0.55 and 0.70 for the original data, revealed the nonlinear property of the dynamic ventilation. DSC analysis showed the same trend. To reduce the errors if motion artifacts are present, the phases without serious mushroom artifacts may be used. To minimize the effect of the nonlinearity in dynamic ventilation, the calculation phase should be chosen as close to the end-inspiration as possible.

4-Dimensional MRI and Attenuation Map Generation in PET/MRI with 4-Dimensional PET-Derived Deformation Matrices: Study of Feasibility for Lung Cancer Applications.

Respiratory motion may reduce accuracy in the fusion of functional and anatomic images from combined PET/MRI systems. Methodologies for the correction of respiratory motion in PET acquisitions with such systems are mostly based on the use of respiration-synchronized MRI acquisitions to derive motion fields. Existing approaches based on tagging acquisitions may introduce artifacts in MR images, whereas motion model approaches require the acquisition of training datasets. The objective of this work was to investigate the possibility of generating 4-dimensional (4D) MR images and associated attenuation maps (AMs) from the combination of a single static MR image and motion fields obtained from simultaneously acquired 4D non-attenuation-corrected (NAC) PET images. Methods: Four-dimensional PET/MRI datasets were acquired for 11 patients on a simultaneous PET/MRI system. The 4D PET datasets were retrospectively binned into 4 motion amplitude frames corresponding to the simultaneously acquired T1-weighted 4D MR images. A T1-weighted 3-dimensional MRI sequence with Dixon-based fat and water separation was also acquired at the end of expiration for PET attenuation correction purposes. All reconstructed 4D NAC PET images were then elastically registered to the single end-of-expiration NAC PET image. The derived motion fields were subsequently applied to the end-of-expiration frame of the acquired 4D MRI volume and the AM derived from the Dixon MR image to generate respiration-synchronized MR images and corresponding AMs. Results: The accuracy of the proposed method was assessed by comparing the generated and acquired images according to metrics such as overall correlation coefficients and differences in distances of anatomic landmarks on the generated and acquired MRI datasets. High correlation coefficients (mean ± SD: 0.93 ± 0.03) and small differences (2.69 ± 0.5 mm) were obtained. Moreover, small tissue classification differences (2.23% ± 0.68%) between generated and 4D MRI-extracted AMs were observed. Conclusion: Our results confirm the feasibility of using 4D NAC PET images for accurate PET attenuation correction and respiratory motion correction in PET/MRI, without the need for patient-specific 4D MRI acquisitions.

Reconstruction-Incorporated Respiratory Motion Correction in Clinical Simultaneous PET/MR Imaging for Oncology Applications.

Simultaneous PET and MR imaging is a promising new technique allowing the fusion of functional (PET) and anatomic/functional (MR) information. In the thoracic-abdominal regions, respiratory motion is a major challenge leading to reduced quantitative and qualitative image accuracy. Correction methodologies include the use of gated frames that lead to low signal-to-noise ratio considering the associated low statistics. More advanced correction approaches, previously developed for PET/CT imaging, consist of either registering all the reconstructed gated frames to the reference frame or incorporating motion parameters into the iterative reconstruction process to produce a single motion-compensated PET image. The goal of this work was to compare these two—previously implemented in PET/CT—correction approaches within the context of PET/MR motion correction for oncology applications using clinical 4-dimensional PET/MR acquisitions. Two different correction approaches were evaluated comparing the incorporation of elastic transformations extracted from 4-dimensional MR imaging datasets during PET list-mode image reconstruction to a postreconstruction image-based approach. Eleven patient datasets acquired on a PET/MR system were used. T1-weighted 4D MR images were registered to the end-expiration image using a nonrigid B-spline registration algorithm to derive deformation matrices accounting for respiratory motion. The derived matrices were subsequently incorporated within a PET image reconstruction of the original emission list-mode data (reconstruction space [RS] method). The corrected images were compared with those produced by applying the deformation matrices in the image space (IS method) followed by summing the realigned gated frames, as well as with uncorrected motion-averaged images. Both correction techniques led to significant improvement in accounting for respiratory motion artifacts when compared with uncorrected motion-averaged images. These improvements included signal-to-noise ratio (mean increase of 28.0% and 24.2% for the RS and IS methods, respectively), lesion size (reduction of 60.4% and 47.9%, respectively), lesion contrast (increase of 70.1% and 57.2%, respectively), and lesion position (changes of 60.9% and 46.7%, respectively). Our results demonstrate significant respiratory motion compensation using both methods, with superior results from a 4D PET RS approach.

The use of a generalized reconstruction by inversion of coupled systems (GRICS) approach for generic respiratory motion correction in PET/MR imaging

Respiratory motion is a source of artifacts in multimodality imaging such as PET/MR. Solutions include retrospective or prospective gating. They have however found limited use in clinical practice, since their increased overall acquisition duration to maintain overall image quality. More elaborate methods consist of using 4D MR datasets to extract spatial deformations in order to correct for the respiratory motion in PET. The main drawbacks of such approaches is the relatively long acquisition times associated with 4D MR imaging which is often incompatible with clinical PET/MR protocols. The objective of this work was to overcome these limitations by exploiting a generalized reconstruction by inversion of coupled systems (GRICS) approach. The methodology is based on a joint estimation of motion during the MR image reconstruction process, providing internal structure motion and associated deformation matrices for retrospective use in PET respiratory motion correction. This method was first validated on four MR volunteers and two PET/MR patient datasets by comparing GRICS generated MR images to 4D MR series obtained by retrospective gating. In a second step 4D PET datasets corresponding to acquired 4D MR images were simulated using the GATE Monte Carlo simulation platform. GRICS generated deformation matrices were subsequently used to correct respiratory motion in comparison to the 4D MR image based deformations both for the simulated and the two 4D PET/MR patient datasets. Results confirm that GRICS synchronized MR images correlate well with the acquired 4D MR series. Similarly, the use of GRICS for respiratory motion correction allows an equivalent percentage improvement on lesion contrast, position and size, considering the PET simulated tumors as well as PET real tumors. This work demonstrates the potential interest of using GRICS for PET respiratory motion correction in combined PET/MR using shorter duration acquisitions without the need for 4D MRI and associated specific MR sequences.

Conversion of parabolic trough mirror shape results measured in different laboratory setups

Shape accuracy of mirror panels for parabolic trough solar collectors has a significant impact on the optical performance of the collectors in a solar power plant and is therefore carefully assessed by test laboratories and manufacturers. Relevant deformation is induced by gravity or mounting forces, so that shape accuracy data measured in different setups cannot be compared.This paper presents a method for conversion of shape measured in a vertical laboratory setup into data for a horizontal laboratory setup. Characteristic deformation matrices for parabolic trough mirror panels of RP3 geometry are determined by deflectometric shape measurements on various mirror panels and by validated finite element analyses (FEA).The resulting root mean square (rms) of measured slope deviation difference (i.e. the gravity induced deformation) between vertical and horizontal setup is on average 2.4mrad for inner mirrors and 1.25mrad for outer mirrors loosely positioned on a frame.Measured data from vertical setup, transformed by such characteristic deformation matrices into horizontal shape results, differ by less than 0.2mrad in rms slope deviation value from data measured in horizontal setup. Whereas the presented approach to convert shape accuracy measurement results is suitable for the calculation of rms values, some of the analyzed mirror samples show differences in local slope deviation values larger than the deflectometric measurement uncertainty. The amount of deviation depends on details of the accuracy of the positioning of the mirrors on the measurement frame and is affected by the fixation and associated mounting forces at the pads.

Motion Freeze for Respiration Motion Correction in PET/CT: A Preliminary Investigation With Lung Cancer Patient Data

Purpose. Respiratory motion presents significant challenges for accurate PET/CT. It often introduces apparent increase of lesion size, reduction of measured standardized uptake value (SUV), and the mismatch in PET/CT fusion images. In this study, we developed the motion freeze method to use 100% of the counts collected by recombining the counts acquired from all phases of gated PET data into a single 3D PET data, with correction of respiration by deformable image registration. Methods. Six patients with diagnosis of lung cancer confirmed by oncologists were recruited. PET/CT scans were performed with Discovery STE system. The 4D PET/CT with the Varian real-time position management for respiratory motion tracking was followed by a clinical 3D PET/CT scan procedure in the static mode. Motion freeze applies the deformation matrices calculated by optical flow method to generate a single 3D effective PET image using the data from all the 4D PET phases. Results. The increase in SUV and decrease in tumor size with motion freeze for all lesions compared to the results from 3D and 4D was observed in the preliminary data of lung cancer patients. In addition, motion freeze substantially reduced tumor mismatch between the CT image and the corresponding PET images. Conclusion. Motion freeze integrating 100% of the PET counts has the potential to eliminate the influences induced by respiratory motion in PET data.

Non rigid respiratory motion correction in whole body PET/MR imaging

Respiratory motion in PET/MR imaging leads to reduced quantitative and qualitative image accuracy. Correction methodologies include the use of respiratory synchronized gated frames which lead to low signal to noise ratio (SNR) given that each frame contains only part of the count available throughout an average PET acquisition. In this work, 4D MRI extracted elastic transformations were applied to list-mode data either inside the image reconstruction or to the reconstructed respiratory synchronized images to obtain respiration corrected PET images. Five patient datasets acquired on the SIEMENS mMR PET/MR system were used. T1-weighted 4D MR images were registered to the end expiration MR image using an elastic B-spline registration algorithm to derive deformation matrices used to account for the respiratory motion. The derived matrices were subsequently applied during the List Mode OSEM PET image reconstruction of the original emission list-mode data. The corrected images were compared with those produced by applying the elastic transformation after reconstructing PET frames followed by summing the realigned gated frames, as well as with uncorrected motion averaged images. Significant improvement was obtained by using any of the two respiratory motion correction techniques compared to uncorrected motion average images (>30% differences in tumor position and size and 25% SNR increase). Both correction approaches lead to nearly equivalent improvements (differences of <8% and <6% for the lesion FWHM and the SNR respectively). A list-mode reconstruction based respiratory motion correction for PET has been implemented and its performance evaluated. This approach was based on the use of elastic transformations derived from 4D MRI during PET image reconstrucion. Our results show significant respiratory motion compensation when compared to the motion average PET images, with slightly better contrast and SNR compared to an equivalent 4D PET image space elastic motion correction method.

Noiseless Vlasov–Poisson simulations with linearly transformed particles

We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.

Motion freeze for respiration motion correction in PET/CT: a preliminary investigation with lung cancer patient data.

Purpose. Respiratory motion presents significant challenges for accurate PET/CT. It often introduces apparent increase of lesion size, reduction of measured standardized uptake value (SUV), and the mismatch in PET/CT fusion images. In this study, we developed the motion freeze method to use 100% of the counts collected by recombining the counts acquired from all phases of gated PET data into a single 3D PET data, with correction of respiration by deformable image registration. Methods. Six patients with diagnosis of lung cancer confirmed by oncologists were recruited. PET/CT scans were performed with Discovery STE system. The 4D PET/CT with the Varian real-time position management for respiratory motion tracking was followed by a clinical 3D PET/CT scan procedure in the static mode. Motion freeze applies the deformation matrices calculated by optical flow method to generate a single 3D effective PET image using the data from all the 4D PET phases. Results. The increase in SUV and decrease in tumor size with motion freeze for all lesions compared to the results from 3D and 4D was observed in the preliminary data of lung cancer patients. In addition, motion freeze substantially reduced tumor mismatch between the CT image and the corresponding PET images. Conclusion. Motion freeze integrating 100% of the PET counts has the potential to eliminate the influences induced by respiratory motion in PET data.

Effects of quantum noise in 4D-CT on deformable image registration and derived ventilation data

Quantum noise is common in CT images and is a persistent problem in accurate ventilation imaging using 4D-CT and deformable image registration (DIR). This study focuses on the effects of noise in 4D-CT on DIR and thereby derived ventilation data. A total of six sets of 4D-CT data with landmarks delineated in different phases, called point-validated pixel-based breathing thorax models (POPI), were used in this study. The DIR algorithms, including diffeomorphic morphons (DM), diffeomorphic demons (DD), optical flow and B-spline, were used to register the inspiration phase to the expiration phase. The DIR deformation matrices (DIRDM) were used to map the landmarks. Target registration errors (TRE) were calculated as the distance errors between the delineated and the mapped landmarks. Noise of Gaussian distribution with different standard deviations (SD), from 0 to 200 Hounsfield Units (HU) in amplitude, was added to the POPI models to simulate different levels of quantum noise. Ventilation data were calculated using the ΔV algorithm which calculates the volume change geometrically based on the DIRDM. The ventilation images with different added noise levels were compared using Dice similarity coefficient (DSC). The root mean square (RMS) values of the landmark TRE over the six POPI models for the four DIR algorithms were stable when the noise level was low (SD <150 HU) and increased with added noise when the level is higher. The most accurate DIR was DD with a mean RMS of 1.5 ± 0.5 mm with no added noise and 1.8 ± 0.5 mm with noise (SD = 200 HU). The DSC values between the ventilation images with and without added noise decreased with the noise level, even when the noise level was relatively low. The DIR algorithm most robust with respect to noise was DM, with mean DSC = 0.89 ± 0.01 and 0.66 ± 0.02 for the top 50% ventilation volumes, as compared between 0 added noise and SD = 30 and 200 HU, respectively. Although the landmark TRE were stable with low noise, the differences between ventilation images increased with noise level, even when the noise was low, indicating ventilation imaging from 4D-CT was sensitive to image noise. Therefore, high quality 4D-CT is essential for accurate ventilation images.

SU‐E‐J‐66: Effects of Noise in 4D‐CT On Deformable Image Registration and Derived Ventilation Data

Purpose: Deformable image registration (DIR) and 4D‐CT have been proposed to generate ventilation images. Quantum noise is common in CT images. This study focuses on the effects of noise in 4D‐CT on DIR and the derived ventilation data. Methods: Diffeomorphic morphons (DM), diffeomorphic demons (DD), optical flow and B‐Spline were used to register the end‐inspiration phase to the end‐expiration phase of 6 4D‐CT sets with landmarks delineated on different phases, called point‐validated pixel‐based breathing thorax models (POPI). Landmarks at expiration were mapped to inspiration using DIR deformation matrices (DIRDM) for each POPI model. Target registration errors (TRE) were calculated as the distances between the delineated and the mapped landmarks. Gaussian noise with different standard deviations (SD) of the amplitude was added to the POPI models to simulate different levels of quantum noise. Ventilation estimations were performed by calculating the volume change geometrically, based on the DIRDM. Ventilation images with different CT noise levels were compared using Dice similarity coefficient (DSC). Results: The root mean square (RMS) values of the landmark TRE over the 6 POPI models for the 4 DIR algorithms were stable when the noise level was below SD=150 Hounsfield Units (HU), and increased with the noise level. The most accurate DIR was DD with mean RMS of 1.5±0.5 and 1.8+−0.5 mm at the added noise SD=0 and 200 HU respectively. The DSC values between the ventilation images with and without added noise decreased with the noise level. The most consistent DIR was DM with mean DSC=0.89+− 0.01 and 0.66+−0.02 for the top 50% ventilation volumes with the added noise of 0 and 30, 0 and 200 HU respectively. Conclusion: While the landmark TRE was stable with noise level for low noise, the differences between ventilation images increased, indicating that 4D‐CT based ventilation imaging is sensitive to image noise. This work was partially supported by a grant from the Varian Medical Systems, Inc.

Effects of Noise in 4D CT on Deformable Image Registration and Derived Ventilation Data

Quantum noise is common in CT images and is a persistent problem in accurate ventilation imaging using 4D-CT and deformable image registration (DIR). This study focuses on the effects of noise in 4D-CT on DIR and thereby derived ventilation data. A total of six sets of 4D-CT data with landmarks delineated in different phases, called point-validated pixel-based breathing thorax models (POPI), were used in this study. The DIR algorithms, including diffeomorphic morphons (DM), diffeomorphic demons (DD), optical flow and B-spline, were used to register the inspiration phase to the expiration phase. The DIR deformation matrices (DIRDM) were used to map the landmarks. Target registration errors (TRE) were calculated as the distance errors between the delineated and the mapped landmarks. Noise of Gaussian distribution with different standard deviations (SD), from 0 to 200 Hounsfield Units (HU) in amplitude, was added to the POPI models to simulate different levels