Second order inverse born approximation for diffuse optical tomography

COMPARISON OF EQUIVALENT LINEAR AND NON LINEAR METHODS ON GROUND RESPONSE ANALYSIS: CASE STUDY AT WEST BANGKA SITE. Within the framework of identifying NPP sites, site surveys are performed in West Bangka (WB), Bangka-Belitung Island Province. Ground response analysis of a potential site has been carried out using peak strain profiles and peak ground acceleration. The objective of this research is to compare Equivalent Linear (EQL) and Non Linear (NL) methods of ground response analysis on the selected NPP site (West Bangka) using DeepSoil software. Equivalent linear method is widely used because requires soil data in simple way and short time of computational process. On the other hand, non linear method is capable of representing the actual soil behaviour by considering non linear soil parameter. The results showed that EQL method has similar trends to NL method. At surface layer, the acceleration values for EQL and NL methods are resulted as 0.425g and 0.375g respectively. NL method is more reliable in capturing higher frequencies of spectral acceleration compared to EQL method.

A comparison was made of the linear least-squares method and a nonlinear least-square method of the Langmuir isotherm and pseudo second order kinetic model for the biosorption of methylene blue onto rice husk. The parameters obtained from the linear method and the nonlinear method were different. The error analysis was performed. Results showed that both linear and nonlinear method can be used to fit the experimental data. The nonlinear method may be a better way to obtain the desired parameters.

This survey reviews the recent development of gradient domain mesh deformation method. Different to other deformation methods, the gradient domain deformation method is a surface-based, variational optimization method. It directly encodes the geometric details in differential coordinates, which are also called Laplacian coordinates in literature. By preserving the Laplacian coordinates, the mesh details can be well preserved during deformation. Due to the locality of the Laplacian coordinates, the variational optimization problem can be casted into a sparse linear system. Fast sparse linear solver can be adopted to generate deformation result interactively, or even in real-time. The nonlinear nature of gradient domain mesh deformation leads to the development of two categories of deformation methods: linearization methods and nonlinear optimization methods. Basically, the linearization methods only need to solve the linear least-squares system once. They are fast, easy to understand and control, while the deformation result might be suboptimal. Nonlinear optimization methods can reach optimal solution of deformation energy function by iterative updating. Since the computation of nonlinear methods is expensive, reduced deformable models should be adopted to achieve interactive performance. The nonlinear optimization methods avoid the user burden to input transformation at deformation handles, and they can be extended to incorporate various nonlinear constraints, like volume constraint, skeleton constraint, and so on. We review representative methods and related approaches of each category comparatively and hope to help the user understand the motivation behind the algorithms. Finally, we discuss the relation between physical simulation and gradient domain mesh deformation to reveal why it can achieve physically plausible deformation result.

The complex, nonlinear and non-stationary electroencephalogram (EEG) signals are very tedious to interpret visually and highly difficult to extract the significant features from them. The linear and nonlinear methods are effective in identifying the changes in EEG signals for the detection of depression. Linear methods do not exhibit the complex dynamical variations in the EEG signals. Hence, chaos theory and nonlinear dynamic methods are widely used in extracting the EEG signal features for computer-aided diagnosis (CAD) of depression. Hence, this article presents the recent efforts on CAD of depression using EEG signals with a focus on using nonlinear methods. Such a CAD system is simple to use and may be used by the clinicians as a tool to confirm their diagnosis. It should be of a particular value to enable the early detection of depression.

Generally speaking, the navigation of underwater targets is solved by the principle of spherical intersection. The number of array elements required for this method is fixed, but in the case of redundant array elements, they can’t be fully utilized. This paper presents two optimization methods based on redundancy measurement. One approach is the Gauss-Newton method and the other is Non linear Optimization method. The former, a non-linear least-squares optimization method that constantly revise regression coefficients through multiple iterations to minimize the sum of squared residuals, and the later, getting least squares solution of non linear redundant equations based on penalty constants. Simulation show that both methods are greatly affected by the initial position, the closer the distance between initial position to the target is, the smaller navigation error is. Under the same simulation conditions, the navigation accuracy of these two methods is higher than that of the ordinary spherical intersection method. The experiment proves these two methods can satisfy the navigation accuracy of the experiment in actual project.

We present high spatial density, multi-modal, parallel-plate Diffuse Optical Tomography (DOT) imaging systems for the purpose of breast tumor detection. One hybrid instrument provides time domain (TD) and continuous wave (CW) DOT at 64 source fiber positions. The TD diffuse optical spectroscopy with PMT- detection produces low-resolution images of absolute tissue scattering and absorption while the spatially dense array of CCD-coupled detector fibers (108 detectors) provides higher-resolution CW images of relative tissue optical properties. Reconstruction of the tissue optical properties, along with total hemoglobin concentration and tissue oxygen saturation, is performed using the TOAST software suite. Comparison of the spatially-dense DOT images and MR images allows for a robust validation of DOT against an accepted clinical modality. Additionally, the structural information from co-registered MR images is used as a spatial prior to improve the quality of the functional optical images and provide more accurate quantification of the optical and hemodynamic properties of tumors. We also present an optical-only imaging system that provides frequency domain (FD) DOT at 209 source positions with full CCD detection and incorporates optical fringe projection profilometry to determine the breast boundary. This profilometry serves as a spatial constraint, improving the quality of the DOT reconstructions while retaining the benefits of an optical-only device. We present initial images from both human subjects and phantoms to display the utility of high spatial density data and multi-modal information in DOT reconstruction with the two systems.

Diffuse optical tomography(DOT) is a nonlinear optimization problem to find optical coefficients using near-infrared light. Linearized methods was used by many researchers to avoid the nonlinearity of DOT. In this paper, the nonlinearity of DOT is studied using Born expansion and some parameters measuring the nonlinearity of DOT is suggested.

Diffuse optical tomography is used to find the optical parameters of a turbid medium with infrared red light. The problem is mathematically formulated as a nonlinear problem to find the solution for the diffusion operator mapping the optical coefficients to the photon density distribution on the boundary of the region of interest, which is also represented by the Born expansion with respect to the unperturbed photon densities and perturbed optical coefficients. We suggest a new method of finding the solution by using the second‐order Born approximation of the operator. The error analysis for the suggested method based on the second‐order Born approximation is presented and compared with the conventional linearized method based on the first‐order Born approximation. The suggested method has better convergence order than the linearized method, and this is verified in the numerical implementation.

Linear and non-linear regression analysis for the sorption kinetics of methylene blue onto activated carbon

Background/Introduction Prior studies revealed exposure to ambient air pollution would increase cardiovascular disease–related mortality and nonfatal events, but the underlying mechanism was not fully elucidated. Disruption of autonomic regulation might be a possible cause of increased cardiovascular morbidity and mortality, but previous work showed inconsistent relationship between ambient air pollution and heart rate variability analyzed by traditional linear methods. Our previous study showed the relationship between ambient air pollution and home blood pressure was non-linear, thus non-linear methods, such as detrended fluctuation analysis (DFA) and multi-scale entropy (MSE), could be more useful tools while assessing the effect of ambient air pollution on biomedical parameters. Purpose To use both traditional linear and novel non-linear methods to evaluate the impact of ambient air pollution on 24-hour heart rate variability. Methods From 2015/01 to 2015/12, patients undergoing 24-hour Holter ECG study in a tertiary medical center were enrolled as the study population. The patients were divided into two groups based on the severity of air pollution in their living areas (severe and mild air pollution groups). The two groups were matched by propensity-score matching. Linear and non-linear methods, including DFA and MSE, were used to calculate 24-hour heart rate variability. Results A total of 568 patients (284 patients in each group) were enrolled in this study. Traditional linear analysis of HRV didn’t show significant difference between the two groups regarding any time- or frequency-domain parameters. In non-linear analysis of HRV, DFA failed to detect significant difference between the two groups, while most MSE parameters (Area1-5, Ln_Area1-5, Area6-20 and Ln_Area6-20) were significantly lower in the severe air pollution group. The MSE analysis revealed significant differences across all scales (1 to 20). Conclusion(s) Ambient air pollution was associated with decreased 24-hour heart rate variability, and the impact was better evaluated by non-linear analysis (specifically multi-scale entropy) than traditional linear method.Table Figure

A crucial parameter in Diffuse Optical Tomography (DOT) is the construction of an accurate forward model, which greatly depends on tissue boundary. Since photon propagation is a three-dimensional volumetric problem, extraction and subsequent modeling of three-dimensional boundaries is essential. Original experimental demonstration of the feasibility of DOT to reconstruct absorbers, scatterers and fluorochromes used phantoms or tissues confined appropriately to conform to easily modeled geometries such as a slab or a cylinder. In later years several methods have been developed to model photon propagation through diffuse media with complex boundaries using numerical solutions of the diffusion or transport equation (finite elements or differences) or more recently analytical methods based on the tangent-plane method . While optical examinations performed simultaneously with anatomical imaging modalities such as MRI provide well-defined boundaries, very limited progress has been done so far in extracting full-field (360 degree) boundaries for in-vivo three-dimensional DOT stand-alone imaging. In this paper, we present a desktop multi-spectrum in-vivo 3D DOT system for small animal imaging. This system is augmented with Technest's full-field 3D cameras. The built system has the capability of acquiring 3D object surface profiles in real time and registering 3D boundary with diffuse tomography. Extensive experiments are performed on phantoms and small animals by our collaborators at the Center for Molecular Imaging Research (CMIR) at Massachusetts General Hospital (MGH) and Harvard Medical School. Data has shown successful reconstructed DOT data with improved accuracy.

Diffuse optical tomography is a novel imaging technique that resolves and quantifies the optical properties of objects buried in turbid media. Typically, numerical solutions of the diffusion equation are employed to construct the tomographic problem when media of complex geometries are investigated. Numerical methods offer implementation simplicity but also significant computation burden, especially when large three-dimensional reconstructions are involved. We present an alternative method of performing tomography of diffuse media of arbitrary geometries by means of an analytical approach, the Kirchhoff approximation. We show that the method is extremely efficient in computation times and consider its potential as a real-time three-dimensional imaging tool.

Born expansion and Fréchet derivatives in nonlinear Diffuse Optical Tomography

Background: Individuals with spinal cord injury (SCI) lose their abilities to stand. The effectiveness of compensating strategies such as the use of various orthosis is studied by stability analysis. These kind of analyses are usually studied by linear method. In this study, the standing stability of complete and incomplete SCI individuals is evaluated by linear versus non-linear methods. Methods: Study groups consisted of 10 normal, 5 incomplete and 5 complete SCI individuals. SCI participants stood with crutch and/or orthosis on a Kistler force plate. The excursions of center of pressure (COP), velocity of COP, correlation dimension, and approximate entropy in the anteroposterior and mediolateral planes were calculated in this study. Statistical analysis was done by one-way ANOVA and Post-hoc calculations by Tukey HSD. Results: Linear method revealed that the difference in “the mediolateral COP sway” and “anteroposterior COP velocity” was insignificant among the groups, whilst the difference in “anteroposterior COP sway”, “mediolateral COP velocity” and “total velocity” was significant. In contrast, non-linear method revealed that the difference in “mediolateral embedding diversion”, “anteroposterior embedding diversion”, “mediolateral correlation dimension” and “anteroposterior ApEn” was insignificant among the groups, whilst the difference in “anteroposterior correlation dimension” and “mediolateral ApEn” was significant. Conclusion: Based on linear method, the stability of SCI subjects seems to be like normal subjects. However, non-linear analysis revealed that although SCI patients knew how to put their body in a good posture to have a stable position, they had no abilities to control their posture.

Solubility data for 930 diverse compounds have been analyzed using linear Partial Least Square (PLS) and nonlinear PLS methods, Continuum Regression (CR), and Neural Networks (NN). 1D and 2D descriptors from MOE package in combination with E-state or ISIS keys have been used. The best model was obtained using linear PLS for a combination between 22 MOE descriptors and 65 ISIS keys. It has a correlation coefficient (r2) of 0.935 and a root-mean-square error (RMSE) of 0.468 log molar solubility (log S(w)). The model validated on a test set of 177 compounds not included in the training set has r2 0.911 and RMSE 0.475 log S(w). The descriptors were ranked according to their importance, and at the top of the list have been found the 22 MOE descriptors. The CR model produced results as good as PLS, and because of the way in which cross-validation has been done it is expected to be a valuable tool in prediction besides PLS model. The statistics obtained using nonlinear methods did not surpass those got with linear ones. The good statistic obtained for linear PLS and CR recommends these models to be used in prediction when it is difficult or impossible to make experimental measurements, for virtual screening, combinatorial library design, and efficient leads optimization.