An improved composite ship magnetic field model with ellipsoid and magnetic dipole arrays

In order to simultaneously maintain the ship magnetic field modeling accuracy, reduce the number of coefficient matrix conditions and the model computational complexity, an improved composite model is designed by introducing the magnetic dipole array model with a single-axis magnetic moment on the basis of the hybrid ellipsoid and magnetic dipole array model. First, the improved composite model of the ship's magnetic field is established based on the magnetic dipole array model with 3-axis magnetic moment, the magnetic dipole array model with only x-axis magnetic moment, and the ellipsoid model. Secondly, the set of equations for calculating the magnetic moments of the composite model is established, and for the problem of solving the pathological set of equations, the least-squares estimation, stepwise regression method, Tikhonov, and truncated singular value decomposition regularization methods are introduced in terms of the magnetic field, and generalized cross-validation is used to solve the optimal regularization parameters. Finally, a ship model test is designed to compare and analyze the effectiveness of the composite and hybrid models in four aspects: the number of coefficient matrix conditions of the model equation set, the relative error of magnetic field fitting, the relative error of magnetic field extrapolation, and the computational time complexity. The modeling results based on the ship model test data show that the composite model can be used for modeling the magnetic field of ships, and compared with the hybrid model, it reduces the number of coefficient matrix conditions and improves the computational efficiency on the basis of retaining a higher modeling accuracy, and it can be effectively applied in related scientific research and engineering.

A mathematical framework for the analysis and comparison of contact detection methods for ellipses and ellipsoids

The purpose of this research is to provide a framework for the analysis and comparison of contact detection algorithms for pairs of ellipses and ellipsoids. This work focuses primarily on the category of algorithms that are the most computationally efficient and can produce estimates of the separation and the penetration distance between ellipses and ellipsoids. Specifically, only analytic representations of the ellipses and ellipsoids are considered and contact detection for moving pairs of ellipsoids is not treated. The first contribution is a mathematical framework for the study of these algorithms, most notably with existence and uniqueness proofs for classes of contact detection algorithms, formal descriptions of the asymptotics of pairs of ellipses in close contact (or overlap), and a global analysis of constraints on the normals. The framework highlights the key role played by the different definitions of contact found in the literature, independent of the numerical strategies deployed to estimate the separation/penetration distance. Specifically, it is shown that all the studied algorithms can be expressed as minimization problems, with or without non-binding constraints on the normal(s) at the contact point(s), and that the constraints can be used to identify the global minima among the critical points in the minimization problem. Another contribution of this research, based on the mathematical framework introduced, is a better classification of the known algorithms. These algorithms are compared on established test problems, and their strengths and weaknesses are highlighted and explained in terms of their classification. Furthermore, this research provides comparisons in speed and stability between the most efficient algorithms in each category over a large sample size of test problems. Among the other contributions, this research describes inexpensive but effective initial estimates of the contact to be used in iterative algorithms. Finally, the usefulness of the new framework is illustrated with the introduction of a fast algorithm combining some new and old ideas.

Data on mitochondrial ultrastructure of photoreceptors in pig, rabbit, and mouse retinas

Photoreceptors are one of the most energy-consuming cell types within the human body. To meet their high energy demand, photoreceptors possess a mitochondrial cluster in the inner segment of the cell. Interestingly, in several species, the inner segment of cone photoreceptors contains extremely large mitochondria that exceed 2 µm in diameter, called mega-mitochondria. We previously reported that pig retinas also contain mega-mitochondria, however, there are few reports whether mega-mitochondria are present in mammalian photoreceptors. In the present experiment, we analyzed pig, rabbit, and mouse photoreceptors under a scanning electron microscope (SEM), and compared the mitochondrial morphology. Our data showed that all three species present numerous mitochondrial clusters in the ellipsoid zone of photoreceptors, adjacent to the outer segment. In the pig retina, the inner segments of cone and rod photoreceptors were localized in different layers; consequently, we were able to distinguish them easily. Mega-mitochondria were identified only in the inner segment of cone photoreceptors. Also, mitochondria of cone photoreceptors, including mega-mitochondria, were dense cristae and high electron-densities compared to those of rod photoreceptors. In the rabbit retina, cone photoreceptors were existed within the layer of rod photoreceptor outer segment. The rod photoreceptors had a characteristic long outer segment. Cone photoreceptors had a short outer segment, and also had a thick inner segment compared to rod photoreceptors. Most of the mitochondria present in the rod photoreceptor inner segment were long and narrow, whereas mitochondria of cone photoreceptors were fragmented and short. Mega-mitochondria was not detected in rabbit retina. In the mouse retina, most of the photoreceptor cells were rod photoreceptors. Since the shape of the inner segments were very similar, we distinguished cone and rod photoreceptors based on the shape of the outer segments. Some mitochondria of both rod and cone photoreceptors were long and narrow, and there was no significant difference in mitochondrial morphology. Our data showed that mitochondrial morphology in the inner segment of photoreceptors vary among mammalian species. Although mega-mitochondria were present in pig photoreceptors, we could not observe their presence in rabbit nor mouse retinas. To our knowledge, this is a first experiment that perform the wide field observation of rabbit and mouse retina using electron microscopy, and that compare the mitochondrial morphology of photoreceptor cells in pig, rabbit and mouse.

Defining the shape of the scapulothoracic gliding surface

PURPOSE

The aim of the study is to evaluate the difference in shape of the upper part and lower part of the Scapulothoracic Gliding Surface (STGS).

METHODS

3D-CT images of the thoracic cage of 50 patients were created in MIMICS ^®. Three anatomical landmarks (insertion m. serratus anterior on 5th rib; transverse process of 2th and 7th vertebra) were used as an anteroposterior cutting plane to define the STGS. The upper part of the STG was defined as rib 2-5 and the lower part as 5-8. Next, in MATLAB ^®, a script was used to create the sphere with best fit for upper and lower parts of STGS. The Root-Square-Mean Error (RSME) (mm) between two closest points on the fitted sphere and the STGS of both parts were calculated to determine the goodness-of-fit.

RESULTS

The RSME was found to be significantly lower for the area ribs 2-5 (mean 7.85 mm, SD 1.86) compared the area of ribs 5-8 (mean 10.08 mm, SD 1.90).

CONCLUSION

The STGS of the upper thoracic wall (2-5) is more spherical shaped than the STGS of the lower thoracic wall (rib 5-8).

Improving ultrasound-based prostate volume estimation

Background

To define a new coefficient to be used in the formula (Volume = L x H x W x Coefficient) that better estimates prostate volume using dimensions of fresh prostates from patients who had transrectal ultrasound (TRUS) imaging prior to prostatectomy.

Methods

The prostate was obtained from 153 patients, weighed and measured to obtain length (L), height (H), and width (W). The density was determined by water displacement to calculate volume. TRUS data were retrieved from patient charts. Linear regression analyses were performed to compare various prostate volume formulas, including the commonly used ellipsoid formula and newly introduced bullet-shaped formula.

Results

By relating measured prostate volumes from fresh prostates to TRUS-estimated prostate volumes, 0.66 was the best fitting coefficient in the (L x H x W x Coefficient) equation. This newfound coefficient combined with outlier removal yielded a linear equation with an R² of 0.64, compared to 0.55 and 0.60, for the ellipsoid and bullet, respectively. By comparing each of the measured vs. estimated dimensions, we observed that the mean prostate height and length were overestimated by 11.1 and 10.8% using ultrasound (p < 0.05), respectively, while the mean width was similar (p > 0.05). Overall, the ellipsoid formula underestimates prostate volumes by 18%, compared to an overestimation of 4.6 and 5.7% for the bullet formula and the formula using our coefficient, respectively.

Conclusions

This study defines, for the first time, a coefficient based on freshly resected prostates as a reference to estimate volumes by imaging. Our findings support a bullet rather than an ellipsoid prostate shape. Moreover, substituting the coefficient commonly used in the ellipsoid formula by our calculated coefficient in the equation estimating prostate volume by TRUS, provides a more accurate value of the true prostate volume.

FitEllipsoid: a fast supervised ellipsoid segmentation plugin

BACKGROUND

The segmentation of a 3D image is a task that can hardly be automatized in certain situations, notably when the contrast is low and/or the distance between elements is small. The existing supervised methods require a high amount of user input, e.g. delineating the domain in all planar sections.

RESULTS

We present FitEllipsoid, a supervised segmentation code that allows fitting ellipsoids to 3D images with a minimal amount of interactions: the user clicks on a few points on the boundary of the object on 3 orthogonal views. The quantitative geometric results of the segmentation of ellipsoids can be exported as a csv file or as a binary image. The core of the code is based on an original computational approach to fit ellipsoids to point clouds in an affine invariant manner. The plugin is validated by segmenting a large number of 3D nuclei in tumor spheroids, allowing to analyze the distribution of their shapes. User experiments show that large collections of nuclei can be segmented with a high accuracy much faster than with more traditional 2D slice by slice delineation approaches.

CONCLUSIONS

We designed a user-friendly software FitEllipsoid allowing to segment hundreds of ellipsoidal shapes in a supervised manner. It may be used directly to analyze biological samples, or to generate segmentation databases necessary to train learning algorithms. The algorithm is distributed as an open-source plugin to be used within the image analysis software Icy. We also provide a Matlab toolbox available with GitHub.

Impact of hydrophobic micron ellipsoids on liquid surfaces

HYPOTHESIS

Hydrophobic spheres may exhibit three impact modes after impacting the liquid surface. For the impact of common non-spherical particles in practical processes, particle shape affects the flow of surrounding fluid and forces acting on them, thus the impact behaviors of non-spherical particles may differ from those of spherical particles and remain to be revealed.

SIMULATION

The impact of hydrophobic micron ellipsoidal particles is numerically studied by solving the coupled equations of particle motion and surrounding fluid flow combining VOF method and dynamic meshing technique. The motion characteristics of the ellipsoids and fluids, and the main forces acting on the ellipsoids during impact are analyzed.

FINDINGS

The increase in the axis ratio (AR) of ellipsoid decreases the surface tension and fluid force, resulting in a smaller total force acting on the ellipsoid. Correspondingly, the ellipsoid's impact behavior changes. An impact-mode phase diagram is presented for the studied ellipsoids. Three impact modes, namely, submergence, rebound, and oscillation, exist when AR > 0.8, while only submergence and oscillation exist when AR ≤ 0.8. The critical velocities decrease with the increase in AR, which is well illustrated by the analysis of energy conversion under critical conditions.

Development and Evaluation of a Semi-automated Segmentation Tool and a Modified Ellipsoid Formula for Volumetric Analysis of the Kidney in Non-contrast T2-Weighted MR Images

Volumetric analysis of the kidney parenchyma provides additional information for the detection and monitoring of various renal diseases. Therefore the purposes of the study were to develop and evaluate a semi-automated segmentation tool and a modified ellipsoid formula for volumetric analysis of the kidney in non-contrast T2-weighted magnetic resonance (MR)-images. Three readers performed semi-automated segmentation of the total kidney volume (TKV) in axial, non-contrast-enhanced T2-weighted MR-images of 24 healthy volunteers (48 kidneys) twice. A semi-automated threshold-based segmentation tool was developed to segment the kidney parenchyma. Furthermore, the three readers measured renal dimensions (length, width, depth) and applied different formulas to calculate the TKV. Manual segmentation served as a reference volume. Volumes of the different methods were compared and time required was recorded. There was no significant difference between the semi-automatically and manually segmented TKV (p = 0.31). The difference in mean volumes was 0.3 ml (95% confidence interval (CI), -10.1 to 10.7 ml). Semi-automated segmentation was significantly faster than manual segmentation, with a mean difference = 188 s (220 vs. 408 s); p < 0.05. Volumes did not differ significantly comparing the results of different readers. Calculation of TKV with a modified ellipsoid formula (ellipsoid volume × 0.85) did not differ significantly from the reference volume; however, the mean error was three times higher (difference of mean volumes -0.1 ml; CI -31.1 to 30.9 ml; p = 0.95). Applying the modified ellipsoid formula was the fastest way to get an estimation of the renal volume (41 s). Semi-automated segmentation and volumetric analysis of the kidney in native T2-weighted MR data delivers accurate and reproducible results and was significantly faster than manual segmentation. Applying a modified ellipsoid formula quickly provides an accurate kidney volume.

Flocking of quad-rotor UAVs with fuzzy control

This paper investigates the flocking problem of quad-rotor UAVs. Considering the actual situations, we derived a new simplified quad-rotor UAV model which is more reasonable. Based on the model, the T-S fuzzy model of attitude dynamic equation and the corresponding T-S fuzzy feedback controller are discussed. By introducing a double-loop control construction, we adjust its attitude to realize the position control. Then a flocking algorithm is proposed to achieve the flocking of the quad-rotor UAVs. Compared with the flocking algorithm of the mass point model, we dealt with the collision problem of the quad-rotor UAVs. In order to improve the airspace utilization, a more compact configuration called quasi e-lattice is constructed to guarantee the compact flight of the quad-rotor UAVs. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

Computer-Aided tumor diagnosis in 3-D breast elastography

BACKGROUND AND OBJECTIVE

Breast cancer is the major cause of cancer-related mortality in women. However, the death rate can be effectively decreased if the breast cancer can be detected early and treated appropriately. In recent years, many studies have indicated that the elastography has the better diagnosis performance than conventional ultrasound (US).

METHOD

In this study, the 3-D tumor contour is obtained by using the proposed segmentation methods and then the features containing texture information, shape information, ellipsoid fitting information are extracted respectively by using the segmented 3-D tumor contour and B-mode images, and the features containing elasticity information are calculated using the same contour and elastographic images.

RESULTS

In this experiment, totally 40 biopsy-proved lesions containing 20 benign tumors and 20 malignant tumors are used to evaluate the proposed computer-aided diagnosis (CAD) system. From the experimental results, the combination of shape, ellipsoid fitting and elastographic features has the best performance with accuracy 90.50% (36/40), sensitivity 85.00% (17/20), specificity 95.00% (19/20), and the area under the ROC curve Az 0.987.

CONCLUSION

The result shows that tumors can be diagnosed more precisely by using the elastography images.

The effect of solvent polarity on wormlike micelles using dipropylene glycol (DPG) as a cosolvent in an anionic/zwitterionic mixed surfactant system

HYPOTHESIS

The behavior/properties of micellar solutions are governed by Coulombic interactions that are influenced by the polarity of the surfactant head groups, hydrophobic tails, and solvent molecules. The addition of co-solvent should have a direct impact on solvent polarity and the size of the micelles are expected to decrease accordingly.

EXPERIMENTS

In this study, a mixed surfactant system is studied composed of a common anionic surfactant, sodium laureth sulfate-1, modified by a zwitterionic surfactant, cocamidopropyl betaine in deuterated water. In this system, worm-like micelles (WLMs) are formed. The influence of a co-solvent, dipropylene glycol (DPG) in the present of high salt content, is investigated. DPG primarily modifies the dielectric constant of the solvent.

FINDINGS

It was found that the addition of DPG slightly decreased the micelle radius, but dramatically reduced the persistence length as well as the contour length of the micelles. The relative dependence of contour length on salt concentration is not significantly changed. Thus, it is shown that the self-assembled structure can be tuned by adjusting solvent polarity without affecting the relative tunability of the WLM/ellipsoidal structure through counter ion concentration.

Quadrics and Scherk towers

We investigate the relation between quadrics and their Christoffel duals on the one hand, and certain zero mean curvature surfaces and their Gauss maps on the other hand. To study the relation between timelike minimal surfaces and the Christoffel duals of 1-sheeted hyperboloids we introduce para-holomorphic elliptic functions. The curves of type change for real isothermic surfaces of mixed causal type turn out to be aligned with the real curvature line net.

Optical influence of oil droplets on cone photoreceptor sensitivity

Oil droplets are spherical organelles found in the cone photoreceptors of vertebrates. They are generally assumed to focus incident light into the outer segment, and thereby improve light catch because of the droplets' spherical lens-like shape. However, using full-wave optical simulations of physiologically realistic cone photoreceptors from birds, frogs and turtles, we find that pigmented oil droplets actually drastically reduce the transmission of light into the outer segment integrated across the full visible wavelength range of each species. Only transparent oil droplets improve light catch into the outer segments, and any enhancement is critically dependent on the refractive index, diameter of the oil droplet, and diameter and length of the outer segment. Furthermore, oil droplets are not the only optical elements found in cone inner segments. The ellipsoid, a dense aggregation of mitochondria situated immediately prior to the oil droplet, mitigates the loss of light at the oil droplet surface. We describe a framework for integrating these optical phenomena into simple models of receptor sensitivity, and the relevance of these observations to evolutionary appearance and loss of oil droplets is discussed.

Accuracy and feasibility of estimated tumour volumetry in primary gastric gastrointestinal stromal tumours: validation using semiautomated technique in 127 patients

OBJECTIVES

To validate estimated tumour volumetry in primary gastric gastrointestinal stromal tumours (GISTs) using semiautomated volumetry.

METHODS

In this IRB-approved retrospective study, we measured the three longest diameters in x, y, z axes on CTs of primary gastric GISTs in 127 consecutive patients (52 women, 75 men, mean age 61 years) at our institute between 2000 and 2013. Segmented volumes (Vsegmented) were obtained using commercial software by two radiologists. Estimate volumes (V1-V6) were obtained using formulae for spheres and ellipsoids. Intra- and interobserver agreement of Vsegmented and agreement of V1-6 with Vsegmented were analysed with concordance correlation coefficients (CCC) and Bland-Altman plots.

RESULTS

Median Vsegmented and V1-V6 were 75.9, 124.9, 111.6, 94.0, 94.4, 61.7 and 80.3 cm(3), respectively. There was strong intra- and interobserver agreement for Vsegmented. Agreement with Vsegmented was highest for V6 (scalene ellipsoid, x ≠ y ≠ z), with CCC of 0.96 [95 % CI 0.95-0.97]. Mean relative difference was smallest for V6 (0.6 %), while it was -19.1 % for V5, +14.5 % for V4, +17.9 % for V3, +32.6 % for V2 and +47 % for V1.

CONCLUSION

Ellipsoidal approximations of volume using three measured axes may be used to closely estimate Vsegmented when semiautomated techniques are unavailable.

KEY POINTS

Estimation of tumour volume in primary GIST using mathematical formulae is feasible. Gastric GISTs are rarely spherical. Segmented volumes are highly concordant with three axis-based scalene ellipsoid volumes. Ellipsoid volume can be used as an alternative for automated tumour volumetry.

Computer-aided diagnosis of breast DCE-MRI using pharmacokinetic model and 3-D morphology analysis

Three-dimensional (3-D) dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) consists of a large number of images in different enhancement phases which are used to identify and characterize breast lesions. The purpose of this study was to develop a computer-assisted algorithm for tumor segmentation and characterization using both kinetic information and morphological features of 3-D breast DCE-MRI. An integrated color map created by intersecting kinetic and area under the curve (AUC) color maps was used to detect potential breast lesions, followed by the application of a region growing algorithm to segment the tumor. Modified fuzzy c-means clustering was used to identify the most representative kinetic curve of the whole segmented tumor, which was then characterized by using conventional curve analysis or pharmacokinetic model. The 3-D morphological features including shape features (compactness, margin, and ellipsoid fitting) and texture features (based on the grey level co-occurrence matrix) of the segmented tumor were obtained to characterize the lesion. One hundred and thirty-two biopsy-proven lesions (63 benign and 69 malignant) were used to evaluate the performance of the proposed computer-aided system for breast MRI. Five combined features including rate constant (kep), volume of plasma (vp), energy (G1), entropy (G2), and compactness (C1), had the best performance with an accuracy of 91.67% (121/132), sensitivity of 91.30% (63/69), specificity of 92.06% (58/63), and Az value of 0.9427. Combining the kinetic and morphological features of 3-D breast MRI is a potentially useful and robust algorithm when attempting to differentiate benign and malignant lesions.