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The Variational Principle (VP) is designed to generate non-folding grids (diffeomorphisms) with prescribed Jacobian determinant (JD) and curl. The solution pool of the original VP is based on an additive formulation and, consequently, is not invariant in the diffeomorphic Lie algebra. The original VP works well when the prescribed pair of JD and curl is calculated from a diffeomorphism, but not necessarily when the prescribed JD and curl are unknown to come from a diffeomorphism. In spite of that, the original VP works effectively in 2D grid generations. To resolve this issue, in this paper, we describe a new version of VP (revised VP), which is based on the composition of transformations and, therefore, is invariant in the Lie algebra. The revised VP seems to have overcome the inaccuracy of the original VP in 3D grid generations. In the following sections, the mathematical derivations are presented. It is shown that the revised VP can calculate the inverse transformation of a known diffeomorphism. Its inverse consistency and transitivity of transformations are also demonstrated numerically. Finally, a new definition of averaging diffeomorphisms based on the revised VP is proposed.

Medical image segmentation annotated by experts provides the labeled data sets for many scientific researches. However, due to the unevenly experienced backgrounds of the experts and limited numbers of patients with certain diseases or illnesses, not only do such labeled data sets have smaller samples but their quality and normality also can range in wide variabilities and be ambiguous. In practice, these segmentations are usually assigned to be the ground truths for the scientific studies, so it may undermine the trustworthiness of the resulting findings. Therefore, it is meaningful to consider how to give a more unified opinion of the annotations among different experts. In this paper, a novel approach to form normal distributions of segmentation is proposed based on multiple doctors’ annotations for the same patient. The proposed approach is developed through the following steps: (1) utilize a framework(7) of averaging images to construct an averaged annotation based on different given annotations; (2) determine the image registration deformations from the averaged annotation to the given annotations; (3) build a joint multivariate Gaussian distribution over the logorithm of Jacobian determinants and curls of the registration deformations; lastly, (4) simulate a normal distribution of segmentation by the joint Gaussian distribution of registration deformation. This work translates the problem of forming a normal distribution of the image segmentation into a problem of forming joint Gaussian distribution of image registration deformations, which the latter can be reasoned by Jacobian determinant (models local size of pixel cells) and curl (models local rotation of pixel cells) information. In the following sections, a detailed walk-through of the proposed approach is provided along with its analytical mathematics and numerical examples for its effectiveness. A synthetic example of 3 manually defined label image is made to show how to construct a mean label image, and an example of a real cancer image annotated by 3 doctors demonstrates the formation of the normal distribution and the effectiveness of the propose method.

Accurate registration of medical images is vital for doctor’s diagnosis and quantitative analysis. In this paper, we propose a new unsupervised learning network SA-VoxelMorph for 3D deformable medical image registration. In this paper, we design a novel network architecture SAU-Net by introducing a new Binary Spatial Attention Module (BSAM) into skip connection of 3D U-Net, which can make full use of the spatial information extracted from the encoding and corresponding decoding stage. Moreover, from variational method, control function can better control the generation of registration field $\phi$. Therefore, we also propose a new registration loss function with novel smoothing term based on optimal control method to generate better $\phi$. We verify our method on two datasets including ADNI and PPMI, and obtain excellent results on magnetic resonance image (MRI) registration with higher average Dice scores and better diffeomorphic registration fields compared with other state-of-the-art methods. The experimental results show the method can achieve better performance in brain MRI registration.

Accurate segmentation of brain tissue in magnetic resonance images (MRI) is a difficult task due to different types of brain abnormalities. In this paper, we review the deformation method focus on the construction of diffeomorphisms to generate the 2D MRI image grids and extend it to the 3D MRI images, address clearly a new formation of the deformation problem for moving domains and construction of diffeomorphisms through a completely different approach. The idea is to control directly the first order differential operators including the Jacobian determinant (JD), divergence (DIV), and curl vector (CV) generated by the 2D and 3D MRI image grids and use them as CNN channels with other modalities (T1-weighted, T1-IR, and T2-FLAIR) or single T1-weighted modality to improve the performance of brain segmentation. More importantly, we discuss the influence of three optimization parameters to the generation of the 2D and 3D MRI image grids by both theoretical analysis and the numerical experiments. We test this method on the IBSR dataset and MRBrainS18 dataset based on VoxResNet and verify the influence of three parameters on the accuracy of MRI brain segmentation. Finally, we also compare the segmentation performance of our method in three networks, including 2D U-Net, 3D U-Net, and VoxResNet. We believe the proposed method can advance the performance in brain segmentation and clinical diagnosis.

Deformable medical image registration is vital for doctor's diagnosis and quantitative analysis. In this paper, we propose a novel unsupervised learning model (denoted as BSADM) for 3D diffeomorphic medical image registration. Inspired by spatial attention module, we propose a new network architecture BSAU-Net by introducing a novel Binary Spatial Attention Module (BSAM) into skip connection, which can take full advantages of the spatial information extracted from the encoding path and corresponding decoding path. In addition, from variational method in differential geometry, monitor function f is used to control the Jacobian determinant (JD) of registration field ɸ. So, we also propose a novel orientation-consistent regularization loss to penalize the local regions with negative Jacobian determinant, which further encourages the diffeomorphic property of the transformations. We verify our method on two datasets including ADNI and PPMI dataset, and obtain excellent improvement on magnetic resonance (MR) image registration with higher average Dice scores and better diffeomorphic registration.

Recently deep learning-based networks have achieved advanced performance in medical image segmentation. However, the development of deep learning is slow in magnetic resonance image (MRI) segmentation of normal brain tissues. In this paper, inspired by channel attention module, we propose a new architecture, Binary Channel Attention U-Net (BCAU- Net), by introducing a novel Binary Channel Attention Module (BCAM) into skip connection of U-Net, which can take full advantages of the channel information extracted from the encoding path and corresponding decoding path. To better aggregate multiscale spatial information of the feature map, spatial pyramid pooling (SPP) modules with different pooling operations are used in BCAM instead of original average-pooling and max-pooling operations. We verify this model on two datasets including IBSR and MRBrainS18, and obtain better performance on MRI brain segmentation compared with other methods. We believe the proposed method can advance the performance in brain segmentation and clinical diagnosis.

Optimization of loss function is one of the research directions in medical image registration. A loss function of registration is the sum of two terms: a similarity term Lsim (Φ) and a smoothing term Lsmooth(Φ). From variational method in differential geometry, control function is essential to generate better registration field Φ. Here, we propose a new registration loss function with novel smoothing terms using VoxelMorph based on control function and Laplacian operator. We divide the process into two steps. The first step is based on Laplacian operator. We replace the gradient of registration field Φ in Lsmooth (Φ) by the Laplacian of Φ. In the second step, we add the term control function F to the Lsmooth (Φ) in the first step, which is the key contribution of our method. We verify our method on two datasets including ADNI and IBSR, and obtain excellent improvement on MR image registration, with better convergence and gets higher average Dice and lower percentage of non-positive Jacobian locations compared with original loss function.

The coils inside the ITER vacuum vessel are part of the overall plasma control system that ensures and maintains stable plasma operations. Two vertical stability coils(VS)will provide fast vertical stabilization of the plasma, while an array of 27 edge localized mode (ELM) coils will create resonant magnetic perturbations to magnetically control the plasma exterior in order to suppress potentially harmful power deposition on plasma-facing components. For magnet coils operating inside of the vacuum vessel, conventional insulation schemes are not an option. After a decade of development and intensive collaboration with industry and research institutes, a copper mineral insulated conductor (MIC) in stainless steel jacket will be used as for its ability to withstand large transient electromagnetic forces, high radiation flux, and high temperature. Complex technologies have been developed by ASIPP for the series of production of IVC conductors, in terms of conductor initial dimension design, MgO block assembly and elaboration of Cu pipe insertion, compaction and winding processes. China has finished all qualification phases, especially for 100-meter unit length conductor manufacturing. The first 100-meter unit length of copper tube is successfully manufactured in China. All conductor samples required for qualification process have successfully passed the electrical tests with good performance. The challenges and status of the production of ITER IVC conductors in China are described in this paper.

316LN stainless steel is selected as a material for Toroidal-field (TF) conductor jacket of International Thermonuclear Experimental Reactor (ITER). When energized, the ITER TF coils experience large pulsed electromagnetic forces that the conductor jacket itself must withstand. The conductor will be compacted, spooled and aged at approximately 650 °C during manufacture. Therefore, the sample jackets were prepared under compaction, stretching and annealing to simulate the manufacturing process and operation of TF coils. The present Chinese TF jacket has good performance under standard conditions. In order to investigate more mechanical properties of 316LN jacket, the different cold working and annealing were applied to the raw materials. The samples were measured at 4.2 K, 77 K and 300 K. Youngs modulus, yield strength (0.2% offset), elongation at failure and SEM images are reported. There is no big deviation among different conditions. The test results show that Chinese TF jacket has good performance.

We propose a new nonrigid registration algorithm which is based on the optimal control approach. In our previously proposed methods, the Jacobian determinant and the curl vector were used as control functions. In this algorithm, we use a new set of control functions. A main advantage of using the new controls is that the positivity and normalization of the Jacobian determinant are satisfied automatically. Numerical results on large deformation brain images are provided to show the accuracy and efficiency of the algorithm.

This paper focuses on mechanical tests on the ITER correction coils (CC) and Feeder jacket 316L stainless steel material. During manufacture, the conductor will be compacted and spooled after cable insertion. Therefore, sample jackets were prepared under compaction in order to simulate the status of conductor during manufacturing. Yield strength (0.2% offset), ultimate tensile strength, Young's modulus and elongation at failure shall be reported. The mechanical properties of materials were measured at 300 K and low temperature (

The China Fusion Engineering Test Reactor (CFETR) is a new tokamak device, whose magnet system includes the toroidal field, central solenoid (CS), and poloidal field coils. To develop the manufacturing technique for the full-size CS coil, the Central Solenoid Model Coil (CSMC) project was launched first. The cable-in-conduit conductor used for CFETR CSMC refers to the International Thermonuclear Experimental Reactor CS conductor with the same short twist pitch cable pattern. As the short twist pitch and low void fraction, a higher compaction ratio during cabling is required, and the possibility of damages occurring on strands is increased. After numerical analysis and experimental trials on cabling technology, one short cable sample was manufactured, which shows good results compared with former experimental cables.

Construction of invertible transformations using differential equations is an interesting and challenging mathematical problem with important applications. We briefly review the existing method by means of harmonic maps in 2D and propose a method of constructing differentiable, invertible transformations between domains in two and three dimensions. Preliminary numerical results demonstrate the effectiveness of the method.

Aims. According to Hubble’s classification scheme, lenticular galaxies represent an intermediate evolutionary step between elliptical and spiral galaxies. This evolutionary path predicts that the aspect ratios of both lenticular and spiral galaxies should be smaller than the aspect ratios of their E6 or E7 elliptical predecessors. In contradiction to this prediction, observation has demonstrated that the aspect ratio of lenticular galaxies is larger than its immediate elliptical predecessor. In this paper, we suggest a novel explanation for this inconsistency. Methods. The approach described in this paper is primarily based on analytical methods; however, some numerical methods are also used. Results. Our idea comes from theoretical and experimental results, which show that a small increase in the equatorial diameter of an oblate spheroid with an aspect ratio ≤0.6 surprisingly causes its minor axis to also increase. We demonstrate that the same phenomenon occurs in the isodensity contours of elliptical galaxies given by Miyamoto & Nagai (Miyamoto M., & Nagai R., 1975, PASJ, 27, 533) and in a Maclaurin spheroidal mass in response to the gravitational force generated by a circumferential equatorial disk. Conclusions. The result of this paper is our explanation for the transformation of a disky elliptical galaxy into a lenticular galaxy which in response to rotation and equatorial diameter expansion evolves into a red spiral galaxy. This evolutionary path is consistent with the common environmental location of disky ellipticals, lenticular and red spiral galaxies and explains why elliptical galaxies are generally ≤E4. The proposed evolutionary path is opposite to the generally accepted formation of lenticular galaxies from the merger of spiral galaxies.

A mathematical problem arising from data set alignment is studied. For two given real-valued functions defined on two (2D or 3D) domains, separately, find a transformation between the two domains that optimizes a similarity functional between the functions. Our approach is based on optimal control with PDE (partial differential equation) constraints. Numerical examples are provided to demonstrate the effectiveness of the method.

In this paper a new approach for non-rigid image registration using mutual information is introduced. A fast parametric method for non-rigid registration is developed by adjusting divergence and curl of an intermediate vector field from which the deformation field is computed using finite-central difference method. Mutual information is newly employed as the similarity measure in the gradient-based cost minimization (or mutual information maximization) of the existing registration framework. The huge amount of data associated with MRI is handled by a fully automated multi-resolution scheme. The adaptive grid system naturally distributes more grids to deprived areas. The positive monitor function disallows grid folding and provides a mean to control the ratio of the areas between the original and transformed domain. The flexibility of the adaptive grid allocation could dramatically reduce processing time with quality preserved. Mutual information facilitates robust registration between different image modalities. Different types of joint histogram estimation are compared and integrated with the system. This scheme is applied on dynamic contrast-enhanced breast MRI, which requires the registration algorithm to be non-rigid, contrast-enhanced features preserving. Preliminary experiments show promising results and great potential for future extension.

Two mesh refinement methods are applied to an inviscid test case and the results are compared with the exact solution from gasdynamics theory. One method is a local hrefinement that is native to ANSYS Fluent and the other is an r-refinement method called the deformation method. An insightful, flow-based explanation of the deformation method is provided. Results show that both methods are capable of improving the quality of the solution, but the h-refinement method increases the number of nodes in the domain and changes connectivity information. The deformation method accomplishes similar results by redistributing points within the mesh. The benefits and potential limitations of both methods are discussed.

The China Fusion Engineering Test Reactor (CFETR) is a new tokamak device, whose magnet system includes toroidal field (TF), central solenoid (CS) and poloidal field (PF) coils. The main goal is to build a fusion engineering tokamak reactor with 50–200 MW fusion power and self-sufficiency by blanket, which means that the deuterium–tritium reaction in the plasma produces neutrons and alpha particles, and the neutrons react with the lithium-containing blanket surrounding the plasma, breeding the tritium by lithium–neutron reaction. To develop the manufacturing technique for the full-size CS coil, the Central Solenoid Model Coil (CSMC) project for CFETR was launched first. A Nb3Sn conductor is to be used in the CFETR CSMC, whose design refers to the ITER CS conductor with the same short-twist-pitch cable pattern. Due to the short twist pitch and relatively low void fraction, a high compaction ratio is required during cabling and the risk of strand damage is increased significantly. Although it is impossible to avoid strand deformation for this design, it is crucial to find a way to reduce strand damage as much as possible. A numerical model was used to analyze the causes of strand damage, including variation in twist pitch length as well as different mechanical properties for copper and Nb3Sn strands. Several experiments have been performed to verify the numerical results, including cabling trials for different conditions and critical current (I c) tests on strands with/without deformation. The results show that the numerical analysis is consistent with the experiments and provides the optimal cabling conditions for the CFETR CSMC.

Toroidal field (TF) coil is made of cable-in-conduit conductor (CICC) with an operating current of 68 kA. In total, 900 Nb3Sn strands and 522 copper strands are cabled around the central spiral and then wrapped with stainless-steel tape of 0.1-mm thickness. The cable is then inserted into a jacket under tensile force that is increasing with length of insertion. Insertion and compaction are key technologies injacketing. The tensile force can lead to rotation of a cable, resulting into an increase in a twist pitch. Understanding the twist pitch variation is very important; in particular, the twist pitch of a cable inside a CICC strongly affects properties such as ac loss. In this paper, we present the results of a Chinese TF conductor during manufacture. A rotation sensor and a straight line on the cable surface were used to measure the rotation during insertion and compaction. X-ray was used to check the changed twist pitch during compaction. Short samples were subjected to destructive examination to assess the exact twist pitch. The test results show that the Chinese TF conductor has a slight rotation and very small twist pitch variation during conductor manufacture.

In this paper, we describe the deformation method for generation of moving meshes and its applications in computational fluid dynamics (CFD), and potential applications for image representation, segmentation, and landmark matching for image registration. We demonstrate that the deformation method can generate meshes of prescribed cell area. Numerical examples are presented to confirm that.

We apply the least-squares finite element method with adaptive grid to nonlinear time-dependent PDEs with shocks. The least-squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006