A biplanar reconstruction method based on 2D and 3D contours: application to the distal femur

A three-dimensional (3D) reconstruction algorithm based on contours identification from biplanar radiographs is presented. It requires, as technical prerequisites, a method to calibrate the biplanar radiographic environment and a surface generic object (anatomic atlas model) representing the structure to be reconstructed. The reconstruction steps consist of: the definition of anatomical regions, the identification of 2D contours associated to these regions, the calculation of 3D contours and projection onto the radiographs, the associations between points of the X-rays contours and points of the projected 3D contours, the optimization of the initial solution and the optimized object deformation to minimize the distance between X-rays contours and projected 3D contours. The evaluation was performed on 8 distal femurs comparing the 3D models obtained to CT-scan reconstructions. Mean error for each distal femur was 1 mm.     

Spectral signal-to-noise ratio and resolution assessment of 3D reconstructions

Measuring the quality of three-dimensional (3D) reconstructed biological macromolecules by transmission electron microscopy is still an open problem. In this article, we extend the applicability of the spectral signal-to-noise ratio (SSNR) to the evaluation of 3D volumes reconstructed with any reconstruction algorithm. The basis of the method is to measure the consistency between the data and a corresponding set of reprojections computed for the reconstructed 3D map. The idiosyncrasies of the reconstruction algorithm are taken explicitly into account by performing a noise-only reconstruction. This results in the definition of a 3D SSNR which provides an objective indicator of the quality of the 3D reconstruction. Furthermore, the information to build the SSNR can be used to produce a volumetric SSNR (VSSNR). Our method overcomes the need to divide the data set in two. It also provides a direct measure of the performance of the reconstruction algorithm itself; this latter information is typically not available with the standard resolution methods which are primarily focused on reproducibility alone.     

3D reconstruction of the pelvis from bi-planar radiography

3D personalized models are more and more requested for clinical and biomechanical studies. Techniques based on bi-planar X-rays present the advantage of a low radiation dose for the patient. However, up to now, such techniques have shown limited accuracy in the case of pelvis reconstruction. This study proposes and validates a method providing accurate 3D personalized model of the pelvis from bi-planar X-rays. The algorithm is based on the fast computation of an initial solution followed by local deformations based on 2D anatomical points and contours that are digitized in both radiographs. Results were close to CT-scan reconstructions (mean difference 1.6 mm and differences under 4.3 mm for 95% of the points). Moreover, 3D morphometry of the pelvis could be obtained with an accuracy of 5%. This technique provides 3D patient specific model with a low radiation dose.     

Reconstruction of non-uniformly sampled five-dimensional NMR spectra by signal separation algorithm

A method for five-dimensional spectral reconstruction of non-uniformly sampled NMR data sets is proposed. It is derived from the previously published signal separation algorithm, with major alterations to avoid unfeasible processing of an entire five-dimensional spectrum. The proposed method allows credible reconstruction of spectra from as little as a few hundred data points and enables sensitive resonance detection in experiments with a high dynamic range of peak intensities. The efficiency of the method is demonstrated on two high-resolution spectra for rapid sequential assignment of intrinsically disordered proteins, namely 5D HN(CA)CONH and 5D (HACA)CON(CO)CONH.     

Symmetry-adapted spherical harmonics method for high-resolution 3D single-particle reconstructions

Three-dimensional (3D) reconstruction is the last and an essential step toward high-resolution structural determination in single-particle cryo-electron microscopy (cryoEM). We have implemented a new algorithm for reconstructing 3D structures of macromolecular complexes with icosahedral symmetry from cryoEM images. Icosahedral symmetry-adapted functions (ISAFs) are used to interpolate structural factors in the reciprocal space to generate a 3D reconstruction in spherical coordinates. In our implementation, we introduced a recursive method for deriving higher order ISAFs from three lower order seed functions. We demonstrate improvements of our new method in both the noise suppression and the effective resolution in 3D reconstruction over the commonly used Fourier-Bessel synthesis method introduced by Crowther et al. three decades ago. Our 3D reconstruction method can be extended to macromolecular complexes with other symmetry types and is thus likely to impact future high-resolution cryoEM single-particle reconstruction efforts in general.     

A Fast Image Alignment Approach for 2D Classification of Cryo-EM Images Using Spectral Clustering

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.     

Prediction of electromagnetic field distributions inside biological bodies by using an inverse scattering procedure based on a statistical cooling algorithm

This paper presents an inverse scattering procedure based on a statistical cooling algorithm to predict the electromagnetic field inside a biological body. By knowing only the scattered electric field distribution in a set of observation points external to the biological model, this method seems to be able to predict the electromagnetic field distributions in the investigation domain, minimizing a suitable cost function. To this end, a numerical statistical procedure is used, which allows to treat functions with a large number of unknowns in an efficient manner and to exploit the so called a priori knowledge in the reconstruction process. Some preliminary results are reported, concerning simplified biological geometries, which clearly show the capabilities and effectiveness, and also the current limitations of the proposed approach. Finally, further advances for the proposed imaging technique are indicated and discussed.     

Adaptive Geometric Tessellation for 3D Reconstruction of Anisotropically Developing Cells in Multilayer Tissues from Sparse Volumetric Microscopy Images

The need for quantification of cell growth patterns in a multilayer, multi-cellular tissue necessitates the development of a 3D reconstruction technique that can estimate 3D shapes and sizes of individual cells from Confocal Microscopy (CLSM) image slices. However, the current methods of 3D reconstruction using CLSM imaging require large number of image slices per cell. But, in case of Live Cell Imaging of an actively developing tissue, large depth resolution is not feasible in order to avoid damage to cells from prolonged exposure to laser radiation. In the present work, we have proposed an anisotropic Voronoi tessellation based 3D reconstruction framework for a tightly packed multilayer tissue with extreme z-sparsity (2–4 slices/cell) and wide range of cell shapes and sizes. The proposed method, named as the ‘Adaptive Quadratic Voronoi Tessellation’ (AQVT), is capable of handling both the sparsity problem and the non-uniformity in cell shapes by estimating the tessellation parameters for each cell from the sparse data-points on its boundaries. We have tested the proposed 3D reconstruction method on time-lapse CLSM image stacks of the Arabidopsis Shoot Apical Meristem (SAM) and have shown that the AQVT based reconstruction method can correctly estimate the 3D shapes of a large number of SAM cells.     

Digital holographic microtomography for high‐resolution refractive index mapping of live cells

Quantification of three‐dimensional (3D) refractive index (RI) with sub‐cellular resolution is achieved by digital holographic microtomography (DHμT) using quantitative phase images measured at multiple illumination angles. The DHμT system achieves sensitive and fast phase measurements based on iterative phase extraction algorithm and asynchronous phase shifting interferometry without any phase monitoring or active control mechanism. A reconstruction algorithm, optical diffraction tomography with projection on convex sets and total variation minimization, is implemented to substantially reduce the number of angular scattered fields needed for reconstruction without sacrificing the accuracy and quality of the reconstructed 3D RI distribution. Tomogram of a living CA9‐22 cell is presented to demonstrate the performance of the method. Further, a statistical analysis of the average RI of the nucleoli, the nucleus excluding the nucleoli and the cytoplasm of twenty CA9‐22 cells is performed. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Segmentation of center brains and optic lobes in 3D confocal images of adult fruit fly brains

Automatic alignment (registration) of 3D images of adult fruit fly brains is often influenced by the significant displacement of the relative locations of the two optic lobes (OLs) and the center brain (CB). In one of our ongoing efforts to produce a better image alignment pipeline of adult fruit fly brains, we consider separating CB and OLs and align them independently. This paper reports our automatic method to segregate CB and OLs, in particular under conditions where the signal to noise ratio (SNR) is low, the variation of the image intensity is big, and the relative displacement of OLs and CB is substantial.We design an algorithm to find a minimum-cost 3D surface in a 3D image stack to best separate an OL (of one side, either left or right) from CB. This surface is defined as an aggregation of the respective minimum-cost curves detected in each individual 2D image slice. Each curve is defined by a list of control points that best segregate OL and CB. To obtain the locations of these control points, we derive an energy function that includes an image energy term defined by local pixel intensities and two internal energy terms that constrain the curve’s smoothness and length. Gradient descent method is used to optimize this energy function. To improve both the speed and robustness of the method, for each stack, the locations of optimized control points in a slice are taken as the initialization prior for the next slice. We have tested this approach on simulated and real 3D fly brain image stacks and demonstrated that this method can reasonably segregate OLs from CBs despite the aforementioned difficulties.     

Consideration of sample motion in cryo-tomography based on alignment residual interpolation

Recently, it has been shown that the resolution in cryo-tomography could be improved by considering the sample motion in tilt-series alignment and reconstruction, where a set of quadratic polynomials were used to model this motion. One requirement of this polynomial method is the optimization of a large number of parameters, which may limit its practical applicability. In this work, we propose an alternative method for modeling the sample motion. Starting from the standard fiducial-based tilt-series alignment, the method uses the alignment residual as local estimates of the sample motion at the 3D fiducial positions. Then, a scattered data interpolation technique characterized by its smoothness and a closed-form solution is applied to model the sample motion. The motion model is then integrated in the tomographic reconstruction. The new method improves the tomogram quality similar to the polynomial one, with the important advantage that the determination of the motion model is greatly simplified, thereby overcoming one of the major limitations of the polynomial model. Therefore, the new method is expected to make the beam-induced motion correction methodology more accessible to the cryoET community.     

High-throughput Computer Method for 3D Neuronal Structure Reconstruction from the Image Stack of the Drosophila Brain and Its Applications

Drosophila melanogaster is a well-studied model organism, especially in the field of neurophysiology and neural circuits. The brain of the Drosophila is small but complex, and the image of a single neuron in the brain can be acquired using confocal microscopy. Analyzing the Drosophila brain is an ideal start to understanding the neural structure. The most fundamental task in studying the neural network of Drosophila is to reconstruct neuronal structures from image stacks. Although the fruit fly brain is small, it contains approximately 100 000 neurons. It is impossible to trace all the neurons manually. This study presents a high-throughput algorithm for reconstructing the neuronal structures from 3D image stacks collected by a laser scanning confocal microscope. The proposed method reconstructs the neuronal structure by applying the shortest path graph algorithm. The vertices in the graph are certain points on the 2D skeletons of the neuron in the slices. These points are close to the 3D centerlines of the neuron branches. The accuracy of the algorithm was verified using the DIADEM data set. This method has been adopted as part of the protocol of the FlyCircuit Database, and was successfully applied to process more than 16 000 neurons. This study also shows that further analysis based on the reconstruction results can be performed to gather more information on the neural network.     

Current approach to radial nerve paralysis

LEARNING OBJECTIVES: After studying this article, the participant should be able to: 1. Identify all potential points of radial nerve compression and other likely causes of radial nerve injury. 2. Accurately diagnose both surgical and nonsurgical causes of radial nerve paralysis. 3. Define a safe and effective approach to the surgical release and reconstruction of the radial nerve. Radial nerve paralysis, which can result from a complex humerus fracture, direct nerve trauma, compressive neuropathies, neuritis, or (rarely) from malignant tumor formation, has been reported throughout the literature, with some controversy regarding its diagnosis and management. The appropriate management of any radial nerve palsy depends primarily on an accurate determination of its cause, severity, duration, and level of involvement. The radial nerve can be injured as proximally as the brachial plexus or as distally as the posterior interosseous or radial sensory nerve. This article reviews the etiology, prognosis, and various treatments available for radial nerve paralysis. It also provides a new classification system and treatment algorithm to assist in the management of patients with radial nerve palsies, and it offers a simple, five-step approach to radial nerve release in the forearm.     

Efficient implementation of a filtered back-projection algorithm using a voxel-by-voxel approach

The large amount of image data necessary for high-resolution 3D reconstruction of macromolecular assemblies leads to significant increases in the computational time. One of the most time consuming operations is 3D density map reconstruction, and software optimization can greatly reduce the time required for any given structural study. The majority of algorithms proposed for improving the computational effectiveness of a 3D reconstruction are based on a ray-by-ray projection of each image into the reconstructed volume. In this paper, we propose a novel fast implementation of the "filtered back-projection" algorithm based on a voxel-by-voxel principle. Our version of this implementation has been exhaustively tested using both model and real data. We compared 3D reconstructions obtained by the new approach with results obtained by the filtered Back-Projections algorithm and the Fourier-Bessel algorithm commonly used for reconstructing icosahedral viruses. These computational experiments demonstrate the robustness, reliability, and efficiency of this approach.     

Reconstruction for 3D PET Based on Total Variation Constrained Direct Fourier Method

This paper presents a total variation (TV) regularized reconstruction algorithm for 3D positron emission tomography (PET). The proposed method first employs the Fourier rebinning algorithm (FORE), rebinning the 3D data into a stack of ordinary 2D data sets as sinogram data. Then, the resulted 2D sinogram are ready to be reconstructed by conventional 2D reconstruction algorithms. Given the locally piece-wise constant nature of PET images, we introduce the total variation (TV) based reconstruction schemes. More specifically, we formulate the 2D PET reconstruction problem as an optimization problem, whose objective function consists of TV norm of the reconstructed image and the data fidelity term measuring the consistency between the reconstructed image and sinogram. To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS). Experiments based on Monte Carlo simulated data and real data are conducted as validations. The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).     

头部组织三维核磁共振电阻抗成像算法的仿真研究

文章给出了一种基于核磁共振技术的三维阻抗成像（电导率分布）重构算法,并将该方法应用于人体头部组织电导率分布重构上。该代数重构方法是利用高分辨率的核磁共振成像系统对成像物体进行三维构建和不同组织的边界区分,根据核磁共振系统中测量得到的磁感应强度Bx和By分量并结合有限元数值计算得到的电流密度分布J组成非线性矩阵,通过迭代求解此非线性矩阵,来解决三维电导率分布的重构问题。在三层球头模型（包括头皮、颅骨和大脑）上分别进行的仿真实验结果表明,该算法具有较强的抗噪声能力和较好的收敛性,重构的头部电导率分布图像具有较高的精确性。     

Photogrammetry for 3D digitizing bones of mounted skeletons: Potential and limits

Since the late 20th century, new technologies have provided powerful ways to digitize biological structures in three dimensions (3D). Among those, photogrammetry is a low cost and non-destructive method, which has become increasingly used since the development of the digital camera. Recent studies have demonstrated that reconstructions of isolated elements can be of as high quality as those obtained with laser scanners. Here, we wanted to test the performance of photogrammetry for the quantitative analysis of mounted specimens in museum exhibitions. Indeed, access to material can be an issue in comparative anatomy and, especially, in paleontology. This is notably the case for large, impressive specimens. We performed reconstructions based on acquisitions done under various conditions and also tested the reconstruction performance of two software programs. The resulting 3D models were then compared to a reference object corresponding to the bone of interest digitized with a cutting-edge surface scanner. Our results show that photogrammetry enables quality reconstruction of the almost entire surface of the mounted bone of interest. Photogrammetry thus appears a reliable method perfectly suited to study large specimens exposed in museum gallery.     

Joint surface modeling with thin-plate splines.

Mathematical joint surface models based on experimentally determined data points can be used to investigate joint characteristics such as curvature, congruency, cartilage thickness, joint contact areas, as well as to provide geometric information well suited for finite element analysis. Commonly, surface modeling methods are based on B-splines, which involve tensor products. These methods have had success; however, they are limited due to the complex organizational aspect of working with surface patches, and modeling unordered, scattered experimental data points. An alternative method for mathematical joint surface modeling is presented based on the thin-plate spline (TPS). It has the advantage that it does not involve surface patches, and can model scattered data points without experimental data preparation. An analytical surface was developed and modeled with the TPS to quantify its interpolating and smoothing characteristics. Some limitations of the TPS include discontinuity of curvature at exactly the experimental surface data points, and numerical problems dealing with data sets in excess of 2000 points. However, suggestions for overcoming these limitations are presented. Testing the TPS with real experimental data, the patellofemoral joint of a cat was measured with multistation digital photogrammetry and modeled using the TPS to determine cartilage thicknesses and surface curvature. The cartilage thickness distribution ranged between 100 to 550 microns on the patella, and 100 to 300 microns on the femur. It was found that the TPS was an effective tool for modeling joint surfaces because no preparation of the experimental data points was necessary, and the resulting unique function representing the entire surface does not involve surface patches. A detailed algorithm is presented for implementation of the TPS.     

Segmentation of left ventricle in short-axis echocardiographic sequences by weighted radial edge filtering and adaptive recovery of dropout regions

In this paper, we present a weighted radial edge filtering algorithm with adaptive recovery of dropout regions for the semi-automatic delineation of endocardial contours in short-axis echocardiographic image sequences. The proposed algorithm requires minimal user intervention at the end diastolic frame of the image sequence for specifying the candidate points of the contour. The region of interest is identified by fitting an ellipse in the region defined by the specified points. Subsequently, the ellipse centre is used for originating the radial lines for filtering. A weighted radial edge filter is employed for the detection of edge points. The outliers are corrected by global as well as local statistics. Dropout regions are recovered by incorporating the important temporal information from the previous frame by means of recursive least squares adaptive filter. This ensures fairly accurate segmentation of the cardiac structures for further determination of the functional cardiac parameters. The proposed algorithm was applied to 10 data-sets over a full cardiac cycle and the results were validated by comparing computer-generated boundaries to those manually outlined by two experts using Hausdorff distance (HD) measure, radial mean square error (rmse) and contour similarity index. The rmse was 1.83 mm with a HD of 5.12 ± 1.21 mm. We have also compared our results with two existing approaches, level set and optical flow. The results indicate an improvement when compared with ground truth due to incorporation of temporal clues. The weighted radial edge filtering algorithm in conjunction with adaptive dropout recovery offers semi-automatic segmentation of heart chambers in 2D echocardiography sequences for accurate assessment of global left ventricular function to guide therapy and staging of the cardiovascular diseases.