MR Image Reconstruction Using Block Matching and Adaptive Kernel Methods

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ₁-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ₁-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ₁-regularized parallel imaging methods.     

Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction

Total generalized variation (TGV)-based computed tomography (CT) image reconstruction, which utilizes high-order image derivatives, is superior to total variation-based methods in terms of the preservation of edge information and the suppression of unfavorable staircase effects. However, conventional TGV regularization employs l₁-based form, which is not the most direct method for maximizing sparsity prior. In this study, we propose a total generalized p-variation (TGpV) regularization model to improve the sparsity exploitation of TGV and offer efficient solutions to few-view CT image reconstruction problems. To solve the nonconvex optimization problem of the TGpV minimization model, we then present an efficient iterative algorithm based on the alternating minimization of augmented Lagrangian function. All of the resulting subproblems decoupled by variable splitting admit explicit solutions by applying alternating minimization method and generalized p-shrinkage mapping. In addition, approximate solutions that can be easily performed and quickly calculated through fast Fourier transform are derived using the proximal point method to reduce the cost of inner subproblems. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to validate the efficiency and feasibility of the proposed method. Overall, the proposed method exhibits reasonable performance and outperforms the original TGV-based method when applied to few-view problems.     

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β _k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.     

Modeling distributions of flying insects: effective attraction radius of pheromone in two and three dimensions

The effective attraction radius (EAR) of an attractive pheromone-baited trap was defined as the radius of a passive “sticky” sphere that would intercept the same number of flying insects as the attractant. The EAR for a particular attractant and insect species in nature is easily determined by a catch ratio on attractive and passive (unbaited) traps, and the interception area of the passive trap. The spherical EAR can be transformed into a circular EAR_c that is convenient to use in two-dimensional encounter rate models of mass trapping and mating disruption with semiochemicals to control insects. The EAR_c equation requires an estimate of the effective thickness of the layer where the insect flies in search of mates and food/habitat. The standard deviation (SD) of flight height of several insect species was determined from their catches on traps of increasing heights reported in the literature. The thickness of the effective flight layer (F_L) was assumed to be , because the probability area equal to the height of the normal distribution,, times the F_L is equal to the area under the normal curve. To test this assumption, 2000 simulated insects were allowed to fly in a three-dimensional correlated random walk in a 10-m thick layer where an algorithm caused them to redistribute according to a normal distribution with specified SD and mean at the midpoint of this layer. Under the same conditions, a spherical EAR was placed at the center of the 10-m layer and intercepted flying insects distributed normally for a set period. The number caught was equivalent to that caught in another simulation with a uniform flight density in a narrower layer equal to F_L, thus verifying the equation to calculate F_L. The EAR and F_L were used to obtain a smaller EAR_c for use in a two-dimensional model that caught an equivalent number of insects as that with EAR in three dimensions. This verifies that the F_L estimation equation and EAR to EAR_c conversion methods are appropriate.     

Synthesis and evaluation of technetium-99m monocationic mixed ligand complexes of phenyl substituted/condensed tetradentate schiff's bases and trimethylphosphine

Tc-99m monocationic mixed ligand complexes of phenyl substituted/condensed Schiff's bases, N,N′-ethylene-bis-(benzoylacetone imine) (L_b) or N,N′-ethylene-bis-(salicylaldehyde imine) (L_c) or N,N′-ethylene-bis-(2-hydroxyacetophenone imine) (L_d) and trimethylphosphine were synthesized to determine the influence of the presence of a phenyl group in these tracers on their heart uptake in rats. A new formulation procedure using aq. β-hydroxypropylcyclodextrin (HPB) solution was developed for intravenous administration of nonpolar ^99mTc complexes. Comparison of biodistribution data for the reference ^99mTc complex from N,N′-ethylene-bis-(acetylacetone imine) and trimethylphosphine using HPB formulation and alternate formulation (0.9% saline) showed the same results. Biodistribution of the title ^99mTc complexes, [^99mTc L_b (PMe₃)₂]⁺, [^99mTc L_c (PMe₃)₂]⁺ and [^99mTc L_d (PMe₃)₂]⁺ showed heart-to-blood activity ratios of 1.7, 2.1 and 1.7, respectively, at 15 min post-injection in rats.     

A Reconstruction Method Based on AL0FGD for Compressed Sensing in Border Monitoring WSN System

In this paper, to monitor the border in real-time with high efficiency and accuracy, we applied the compressed sensing (CS) technology on the border monitoring wireless sensor network (WSN) system and proposed a reconstruction method based on approximately l₀ norm and fast gradient descent (AL0FGD) for CS. In the frontend of the system, the measurement matrix was used to sense the border information in a compressed manner, and then the proposed reconstruction method was applied to recover the border information at the monitoring terminal. To evaluate the performance of the proposed method, the helicopter sound signal was used as an example in the experimental simulation, and three other typical reconstruction algorithms 1)split Bregman algorithm, 2)iterative shrinkage algorithm, and 3)smoothed approximate l₀ norm (SL0), were employed for comparison. The experimental results showed that the proposed method has a better performance in recovering the helicopter sound signal in most cases, which could be used as a basis for further study of the border monitoring WSN system.     

Therapeutically optimized rates of drug release can be achieved by varying the drug-to-lipid ratio in liposomal vincristine formulations

The anti-tumor efficacy of liposomal formulations of cell cycle dependent anticancer drugs is critically dependent on the rates at which the drugs are released from the liposomes. Previous work on liposomal formulations of vincristine have shown increasing efficacy for formulations with progressively slower release rates. Recent work has also shown that liposomal formulations of vincristine with higher drug-to-lipid (D/L) ratios exhibit reduced release rates. In this work, the effects of very high D/L ratios on vincristine release rates are investigated, and the antitumor efficacy of these formulations characterized in human xenograft tumor models. It is shown that the half-times (T_1/2) for vincristine release from egg sphingomyelin/cholesterol liposomes in vivo can be adjusted from T_1/2 = 6.1 h for a formulation with a D/L of 0.025 (wt/wt) to T_1/2 = 117 h (extrapolated) for a formulation with a D/L ratio of 0.6 (wt/wt). The increase in drug retention at the higher D/L ratios appears to be related to the presence of drug precipitates in the liposomes. Variations in the D/L ratio did not affect the circulation lifetimes of the liposomal vincristine formulations. The relationship between drug release rates and anti-tumor efficacy was evaluated using a MX-1 human mammary tumor model. It was found that the antitumor activity of the liposomal vincristine formulations increased as D/L ratio increased from 0.025 to 0.1 (wt/wt) (T_1/2 = 6.1-15.6 h respectively) but decreased at higher D/L ratios (D/L = 0.6, wt/wt) (T_1/2 = 117 h). Free vincristine exhibited the lowest activity of all formulations examined. These results demonstrate that varying the D/L ratio provides a powerful method for regulating drug release and allows the generation of liposomal formulations of vincristine with therapeutically optimized drug release rates.     

Validation of a simplified method for muscle volume assessment

The present study investigated the validity of a simplified muscle volume assessment that uses only the maximum anatomical cross-sectional area (ACSA_max), the muscle length (L_M) and a muscle-specific shape factor for muscle volume calculation ( Albracht et al., 2008, J Biomech 41, 2211–2218). The validation on the example of the triceps surae (TS) muscles was conducted in two steps. First L_M, ACSA_max, muscle volume and shape factor were calculated from magnet resonance image muscle reconstructions of the soleus (SO), gastrocnemius medialis (GM) and lateralis (GL) of a group of untrained individuals (n=13), endurance (n=9) and strength trained (n=10) athletes. Though there were significant differences in the muscle dimensions, the shape factors were similar across groups and were in average 0.497±0.026, 0.596±0.030, and 0.556±0.041 for the SO, GM and GL respectively. In a second step, the shape factors were applied to an independent recreationally active group (n=21) to compare the muscle volume assessed by the simplified method to the results from whole muscle reconstructions. There were no significant differences between the volumes assessed by the two methods. In conclusion, assessing TS muscle volume on the basis of the reported shape factors is valid across populations and the root mean square differences to whole muscle reconstruction of 7.9%, 4.8% and 8.3% for SO, GM and GL show that the simplified method is sensitive enough to detect changes in muscle volume in the context of degeneration, atrophy or hypertrophy.     

Synthesis and characterization of a dinuclear ferric complex with redox-active ligands

A dinuclear ferric complex with the redox-active ligand (L^Cl₂)^2- (H₂L^Cl₂ = N,N′-dimethyl-bis(3,5-dichloro-2-hydroxybenzyl)-1,2-diaminoethane), was synthesized and characterized. The two iron(III) ions are six-coordinate in a distorted octahedral environment of the donor set of one (L^Cl₂)²⁻ and one amine and one phenolate donor of a second (L^Cl₂)²⁻, which bridges the two complex halves. The relatively low-symmetric complex 1 crystallizes in the space group R. The crystal structure contains hexagonal, one-dimensional channels parallel to the c axis with diameters of ∼13 Å. The absorption spectrum of 1 exhibits strong characteristic features of p_π → d_π^∗, p_π → d_σ^∗, phenolate-to-metal CTs, and π → π^∗ ligand transitions. Electrochemical studies on 1 reveal the redox-activity of the coordinated ligand (L^Cl₂)²⁻ by showing irreversible oxidative electron-transfer waves. The reductive electron transfers at negative potentials seem to originate from metal-centered processes. A detailed comparison to complexes with similar donor sets provides new insights into the electrochemical properties of these kinds of complexes.     

Cobalt and iron complexes of chiral C1- and C2-terpyridines: Synthesis, characterization and use in catalytic asymmetric cyclopropanation of styrenes

Optically pure C₁- and C₂-terpyridine ligands (L) form cobalt(II) and iron(II) complexes of formula [Co(L)Cl₂] and [Fe(L)Cl₂], respectively, and Iron(III) complexes of formulas [Fe(L)Cl₃]. Structures of three new chiral cobalt(II) and one iron(III) complexes were analysed using X-ray crystal structure analysis. These complexes were shown to be precursor of efficient catalyst for cyclopropanation. Reaction with AgOTf converted the complex to active catalyst, which gave enantioselectivities of up to 76% ee for the trans-isomers and 83% ee for the cis-isomers of styrene cyclopropanes with ethyl diazoacetate. Hammett studies showed the active species for both cobalt and iron complexes to have a non-linear relationship to σ_p constant.     

An Augmented Lagrangian Based Compressed Sensing Reconstruction for Non-Cartesian Magnetic Resonance Imaging without Gridding and Regridding at Every Iteration

Background

Non-Cartesian trajectories are used in a variety of fast imaging applications, due to the incoherent image domain artifacts they create when undersampled. While the gridding technique is commonly utilized for reconstruction, the incoherent artifacts may be further removed using compressed sensing (CS). CS reconstruction is typically done using conjugate-gradient (CG) type algorithms, which require gridding and regridding to be performed at every iteration. This leads to a large computational overhead that hinders its applicability.

Methods

We sought to develop an alternative method for CS reconstruction that only requires two gridding and one regridding operation in total, irrespective of the number of iterations. This proposed technique is evaluated on phantom images and whole-heart coronary MRI acquired using 3D radial trajectories, and compared to conventional CS reconstruction using CG algorithms in terms of quantitative vessel sharpness, vessel length, computation time, and convergence rate.

Results

Both CS reconstructions result in similar vessel length (P = 0.30) and vessel sharpness (P = 0.62). The per-iteration complexity of the proposed technique is approximately 3-fold lower than the conventional CS reconstruction (17.55 vs. 52.48 seconds in C++). Furthermore, for in-vivo datasets, the convergence rate of the proposed technique is faster (60±13 vs. 455±320 iterations) leading to a ∼23-fold reduction in reconstruction time.

Conclusions

The proposed reconstruction provides images of similar quality to the conventional CS technique in terms of removing artifacts, but at a much lower computational complexity.     

The Scaling of Blood Flow Resistance: From a Single Vessel to the Entire Distal Tree

Although the flow resistance of a single vessel segment is easy to compute, the equivalent resistance of a network of vessel segments or the entire vasculature of an organ is difficult to determine in an analytic form. Here, we propose what we believe is a novel resistance scaling law for a vascular tree (i.e., the resistance of a vessel segment scales with the equivalent resistance of the corresponding distal tree). The formulation can be written as (Rs/Rc)∝(Ls/Lc) (where Rs and Ls are the resistance and length of a vessel segment, respectively, and Rc and Lc are the equivalent resistance and total length of the corresponding distal tree, respectively), which was validated for the coronary vascular systems of the heart. The scaling law was also shown to apply to the vascular systems of the lung, mesentery, muscle, eye, and so on. The novel resistance scaling law, coupled with the 3/4-power scaling law for metabolic rates, can predict several structure-function relations of vascular trees, albeit with a different exponent. In particular, the self-similar nature of the scaling law may serve as a diagnostic tool with the help of noninvasive imaging modalities.     

3D Coronary Artery Reconstruction by 2D Motion Compensation Based on Mutual Information

Background

3D reconstruction of the coronary arteries can provide more information in the interventional surgery. Motion compensation is one kind of the 3D reconstruction method.

Methods of least squares and SIRT in reconstruction.

In this paper we show that a particular version of the Simultaneous Iterative Reconstruction Technique (SIRT) proposed by Gilbert in 1972 strongly resembles the Richardson least-squares algorithm.By adopting the adjustable parameters of the general Richardson algorithm, we have been able to produce generalized SIRT algorithms with improved convergence.A particular generalization of the SIRT algorithm, GSIRT, has an adjustable parameter σ and the starting picture ρ⁰ as input. A value $\text{1}\text{2}$ for σ and a weighted back-projection for ρ⁰ produce a stable algorithm.We call the SIRT-like algorithms for the solution of the weighted leastsquares problems LSIRT and present two such algorithms, LSIRT1 and LSIRT2, which have definite computational advantages over SIRT and GSIRT.We have tested these methods on mathematically simulated phantoms and find that the new SIRT methods converge faster than Gilbert's SIRT but are more sensitive to noise present in the data. However, the faster convergence rates allow termination before the noise contribution degrades the reconstructed image excessively.     

Synthesis, crystal structure, and catalytic studies on dinuclear copper(II) mesocates

Imine based bis-bidentate ligands H₂-m-xysal, (L₁H₂); H₂-m-xysal-Cl, (L₂H₂); H₂-m-xysal-Br, (L₃H₂); H₂-m-xysal-OCH_3, (L₄H₂); H₂-m-xysal-(t-Bu)_2, (L₅H₂) were synthesized and characterized. These substituted 1,3-bis(hydroxylbenzyl)-diaminoxylene dianion ligands upon treating with copper(II) acetate in 2:2 equivalent of L:M ratio, resulted in a series of binuclear [Cu₂(m-xysal)₂] neutral complexes 1-5. The crystal structures determined for the complexes 1 and 2 indicate a dinuclear association. The CH?π interaction observed between the metal-chelate ring and the hydrogens associated with m-xylene spacer moiety being first in this series of complexes, is demonstrated to stabilize the helical conformation through intramolecular self assembly process. The position of the resonance on the EPR spectra and the absence of ΔMs = ±1 feature for the complexes 2, 3, and 5 obtained for room temperature solid state samples revealed that the metal centers though exist in the dinuclear unit, they are separated from each other and possess a non-interacting monomer-type metal-metal association. The Cu(II) centers in all these complexes possessing an intermediate geometry between tetrahedral and square planar, an appropriate catalytic study converting 4-nitrobenzaldehye to corresponding nitroaldol was carried out using complex 5.     

Manganese(II) complexes of di-2-pyridinylmethylene-1,2-diimine di-Schiff base ligands: Structures and reactivity

Manganese(II) complexes [Mn(L)X₂] were prepared and characterized, where L is a neutral di-Schiff base ligand incorporating pyridylimine donor arms, including (1R,2R)-N,N′-bis(2-pyridylmethylidene)-1,2-diphenylethylenediimine (L¹), (1R,2R)-N,N′-bis(6-methyl-2-pyridylmethylidene)-1,2-cyclohexyldiimine (L²), or (1R,2R)-, (1S,2S)- or racemic N,N′-bis(2-pyridylmethylidene)-1,2-cyclohexyldiimine (L³), and X⁻ =  or Cl⁻. Product complexes were structurally characterized, specifically including [Mn(R,R-L¹)(NCCH₃)₃](ClO₄)₂, [Mn(R,R-L²)(OH₂)₂](ClO₄)₂ and racemic [Mn(L³)Cl₂]. The first of these complexes features a heptacoordinate ligand field in a distorted pentagonal bipyramid, and the latter two are hexacoordinate, but retain equatorially monovacant pentagonal bipyramidal structures. Complexes [Mn(L³)X₂] (X⁻ = Cl⁻, ) were reacted with the primary phosphine FcCH₂PH₂ (Fc = -C₅H₄FeC₅H₅), H₂O and ethyldiazoacetate (EDA). The first two substrates prompted reactivity at a single ligand imine bond, resulting in hydrophosphination and hydrolysis, respectively. Complexes of the derivative ligands were also structurally characterized. Evidence for EDA activation was obtained by electrospray ionization mass spectrometry, but catalytic carbene transfer was not obtained.     

L-[Methyl-(11C)]-methionine of high enantiomeric purity production via online-11C-methylation of L-homocysteine thiolactone hydrochloride

L-[Methyl-(¹¹C)]Methionine ([¹¹C]MET), labelled with carbon-11 (T _1/2 = 20 min), is the most commonly used amino acid radiotracer for PET diagnostics of brain tumors. The production of [¹¹C]MET via online ¹¹C-methylation of L-homocysteine thiolactone hydrochloride (lactone) on C18 solid phase extraction cartridge creates a problem of insufficient enantiomeric purity (content of L-isomer) of the product. The results of a systematic study of the influence of reaction parameters (lactone/base and the EtOH/H₂O ratios, time of ¹¹C-methylation) on the content of L-isomer in the formulation are presented. The developed method of online [¹¹C]MET synthesis allows to obtain a product with a sufficiently high radiochemical yield (75 ± 3%, n = 100, based on [¹¹C]CH₃I) and reliably high content of L-isomer (93.7 ± 0.5%) satisfying the requirements of clinical applications. [¹¹C]MET synthesis was performed on a fully automated module designed by the Institute of the Human Brain (IHB RAS).     

Exploring Variability in CT Characterization of Tumors: A Preliminary Phantom Study

PURPOSE: To explore the effects of computed tomography (CT) slice thickness and reconstruction algorithm on quantification of image features to characterize tumors using a chest phantom. MATERIALS AND METHODS: Twenty-two phantom lesions of known sizes (10 and 20 mm), shapes (spherical, elliptical, lobulated, and spiculated), and densities [-630, -10, and +100 Hounsfield Unit (HU)] were inserted into an anthropomorphic thorax phantom and scanned three times with relocations. The raw data were reconstructed using six imaging settings, i.e., a combination of three slice thicknesses of 1.25, 2.5, and 5 mm and two reconstruction kernels of lung and standard. Lesions were segmented and 14 image features representing lesion size, shape, and texture were calculated. Differences in the measured image features due to slice thickness and reconstruction algorithm were compared using linear regression method by adjusting three confounding variables (size, density, and shape). RESULTS: All 14 features were significantly different between 1.25 and 5 mm slice images. The 1.25 and 2.5 mm slice thicknesses were better than 5 mm for volume, density mean, density SD gray-level co-occurrence matrix (GLCM) energy and homogeneity. As for the reconstruction algorithm, there was no significant difference in uni-dimension, volume, shape index 9, and compactness. Lung reconstruction was better for density mean, whereas standard reconstruction was better for density SD. CONCLUSIONS: CT slice thickness and reconstruction algorithm can significantly affect the quantification of image features. Thinner (1.25 and 2.5 mm) and thicker (5 mm) slice images should not be used interchangeably. Sharper and smoother reconstructions significantly affect the density-based features.     

Synthesis,Spectral and Antibacterial Studies of Binuclear Titanium(IV) / Zirconium(IV) Complexes of Piperazine Dithiosemicarbazones

The reactions of mono(cyclopentadienyl)titanium(IV) trichloride and bis(cyclopentadienyl)titanium(IV)/ zirconium(IV) dichloride with a new class of dithiosemicarbazone, derived by condensing piperazine dithiosemicarbazide with benzaldehyde (L₁H₂), 2-chlorobenzaldehyde (L₂H₂), 4-nitrobenzaldehyde (L₃H₂) or salicylaldehyde (L₄H₄) have been studied and different types of binuclear products, viz. [{CpTiCl₂}₂L], [{Cp₂MCl}₂L], ((L=L₁, L₂ or L₃), [{CpTiCI}₂L₄] and [{Cp₂M}₂L₄] (M=Yi or Zr), have been isolated. Tentative structures are proposed for these complexes based upon elemental analyses, electrical conductance, magnetic moment and spectral (electronic, IR, ¹H and ¹³C NMR) data. Attempts have been made to establish a correlation between antibacterial activity and the structures of the products.