This study explored the application value of iterative decomposition of water and fatwith echo asymmetry and least-squares estimation(IDEAL-IQ)technology in the early diagnosis of ageing osteoporosis(OP).172 participa...This study explored the application value of iterative decomposition of water and fatwith echo asymmetry and least-squares estimation(IDEAL-IQ)technology in the early diagnosis of ageing osteoporosis(OP).172 participants were enrolled and underwentmagnetic resonance imaging(MRI)examinations on a 3.0T scanner.100 cases were included in the normal group(50 males and 50 females;mean age:45 years;age range:20e84 years).33 cases were included in the osteopenia group(17 males and 16 females;mean age:55 years;age range:43e83 years).39 caseswere includedintheOP group(19males and20females;meanage:58years;age range:48 e82 years).Conventional T1WI and T2WI were first obtained,followed by 3D-IDEAL-IQ-acqui-sition.Fat fraction(FF)and apparent transverse relaxation rate(R2*)resultswere automatically calculated from IDEAL-IQ-images on the console.Based on T1Wand T2W-images,300 ROIs for each participantweremanually delineated in L1-L5 vertebral bodies of five middle slices.In each age group of all normal subjects,each parameter was significantly correlated with gender.In male participants from the normal,osteopenia,and OP groups,statistical analysis revealed F values of 11319.292 and 180.130 for comparisons involving FF and R2*values,respectively(all p<0.0001).The sensitivity and specificity of FF values were 0.906 and 0.950,0.994 and 0.997,0.865 and 0.820,respectively.For R2*,they were 0.665 and 0.616,0.563 and 0.519,0.571 and 0.368,respectively.In female participants from the normal,osteopenia,and OP-groups,statis-tical analysis revealed F values of 12461.658 and 548.274 for comparisons involving FF and R2*values,respectively(all p<0.0001).The sensitivity and specificity of FF values were 0.985 and 0.991,0.996 and 0.996,0.581 and 0.678,respectively.For R2*,they were 0.698 and 0.730,0.603 and 0.665,0.622 and 0.525,respectively.Significant differences were indicated in the quanti-tative values among the three groups.FF value had good performance,while R2*value had poor performance indiscriminatingosteopenia andOP-groups.Overall,the IDEAL-IQ techniqueoffers specific reference indices that enable noninvasive and quantitative assessment of lumbar vertebrae bone metabolism,thereby providing diagnostic information for OP.展开更多
Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics...Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.展开更多
BACKGROUND Iterative decomposition of water and fat with echo asymmetry and least squares estimation quantification sequence(IDEAL-IQ)is based on chemical shift-based water and fat separation technique to get proton d...BACKGROUND Iterative decomposition of water and fat with echo asymmetry and least squares estimation quantification sequence(IDEAL-IQ)is based on chemical shift-based water and fat separation technique to get proton density fat fraction.Multiple studies have shown that using IDEAL-IQ to test the stability and repeatability of liver fat is acceptable and has high accuracy.AIM To explore whether Gadoxetate Disodium(Gd-EOB-DTPA)interferes with the measurement of the hepatic fat content quantified with the IDEAL-IQ and to evaluate the robustness of this technique.METHODS IDEAL-IQ was used to quantify the liver fat content at 3.0T in 65 patients injected with Gd-EOB-DTPA contrast.After injection,IDEAL-IQ was estimated four times,and the fat fraction(FF)and R2* were measured at the following time points:Precontrast,between the portal phase(70 s)and the late phase(180 s),the delayed phase(5 min)and the hepatobiliary phase(20 min).One-way repeated-measures analysis was conducted to evaluate the difference in the FFs between the four time points.Bland-Altman plots were adopted to assess the FF changes before and after injection of the contrast agent.P<0.05 was considered statistically significant.RESULTS The assessment of the FF at the four time points in the liver,spleen and spine showed no significant differences,and the measurements of hepatic FF yielded good consistency between T1 and T2[95%confidence interval:-0.6768%,0.6658%],T1 and T3(-0.3900%,0.3178%),and T1 and T4(-0.3750%,0.2825%).R2* of the liver,spleen and spine increased significantly after injection(P<0.0001).CONCLUSION Using the IDEAL-IQ sequence to measure the FF,we can obtain results that will not be affected by Gd-EOB-DTPA.The high reproducibility of the IDEAL-IQ sequence makes it available in the scanning interval to save time during multiphase examinations.展开更多
This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann con...This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.展开更多
The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sw...The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.展开更多
基金supported by the Planned Project Grant(Grant No.3502Z20199064)from the Science and Technology Bureau of Xiamen(CN)the training project(Grant No.2020GGB067)of the youth and middle-aged talents of Fujian Provincial Health Commission(CN).
文摘This study explored the application value of iterative decomposition of water and fatwith echo asymmetry and least-squares estimation(IDEAL-IQ)technology in the early diagnosis of ageing osteoporosis(OP).172 participants were enrolled and underwentmagnetic resonance imaging(MRI)examinations on a 3.0T scanner.100 cases were included in the normal group(50 males and 50 females;mean age:45 years;age range:20e84 years).33 cases were included in the osteopenia group(17 males and 16 females;mean age:55 years;age range:43e83 years).39 caseswere includedintheOP group(19males and20females;meanage:58years;age range:48 e82 years).Conventional T1WI and T2WI were first obtained,followed by 3D-IDEAL-IQ-acqui-sition.Fat fraction(FF)and apparent transverse relaxation rate(R2*)resultswere automatically calculated from IDEAL-IQ-images on the console.Based on T1Wand T2W-images,300 ROIs for each participantweremanually delineated in L1-L5 vertebral bodies of five middle slices.In each age group of all normal subjects,each parameter was significantly correlated with gender.In male participants from the normal,osteopenia,and OP groups,statistical analysis revealed F values of 11319.292 and 180.130 for comparisons involving FF and R2*values,respectively(all p<0.0001).The sensitivity and specificity of FF values were 0.906 and 0.950,0.994 and 0.997,0.865 and 0.820,respectively.For R2*,they were 0.665 and 0.616,0.563 and 0.519,0.571 and 0.368,respectively.In female participants from the normal,osteopenia,and OP-groups,statis-tical analysis revealed F values of 12461.658 and 548.274 for comparisons involving FF and R2*values,respectively(all p<0.0001).The sensitivity and specificity of FF values were 0.985 and 0.991,0.996 and 0.996,0.581 and 0.678,respectively.For R2*,they were 0.698 and 0.730,0.603 and 0.665,0.622 and 0.525,respectively.Significant differences were indicated in the quanti-tative values among the three groups.FF value had good performance,while R2*value had poor performance indiscriminatingosteopenia andOP-groups.Overall,the IDEAL-IQ techniqueoffers specific reference indices that enable noninvasive and quantitative assessment of lumbar vertebrae bone metabolism,thereby providing diagnostic information for OP.
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.
基金Supported by National Natural Science Foundation of China,No.82272053.
文摘BACKGROUND Iterative decomposition of water and fat with echo asymmetry and least squares estimation quantification sequence(IDEAL-IQ)is based on chemical shift-based water and fat separation technique to get proton density fat fraction.Multiple studies have shown that using IDEAL-IQ to test the stability and repeatability of liver fat is acceptable and has high accuracy.AIM To explore whether Gadoxetate Disodium(Gd-EOB-DTPA)interferes with the measurement of the hepatic fat content quantified with the IDEAL-IQ and to evaluate the robustness of this technique.METHODS IDEAL-IQ was used to quantify the liver fat content at 3.0T in 65 patients injected with Gd-EOB-DTPA contrast.After injection,IDEAL-IQ was estimated four times,and the fat fraction(FF)and R2* were measured at the following time points:Precontrast,between the portal phase(70 s)and the late phase(180 s),the delayed phase(5 min)and the hepatobiliary phase(20 min).One-way repeated-measures analysis was conducted to evaluate the difference in the FFs between the four time points.Bland-Altman plots were adopted to assess the FF changes before and after injection of the contrast agent.P<0.05 was considered statistically significant.RESULTS The assessment of the FF at the four time points in the liver,spleen and spine showed no significant differences,and the measurements of hepatic FF yielded good consistency between T1 and T2[95%confidence interval:-0.6768%,0.6658%],T1 and T3(-0.3900%,0.3178%),and T1 and T4(-0.3750%,0.2825%).R2* of the liver,spleen and spine increased significantly after injection(P<0.0001).CONCLUSION Using the IDEAL-IQ sequence to measure the FF,we can obtain results that will not be affected by Gd-EOB-DTPA.The high reproducibility of the IDEAL-IQ sequence makes it available in the scanning interval to save time during multiphase examinations.
文摘This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.
基金This work is partially supported by Sloan FoundationNSF DMS0513073+1 种基金ONR grant N00014-02-1-0090DARPA grant N00014-02-1-0603
文摘The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms.
