Nonlinear Inversion MR Elastography With Low-Frequency Actuation.

Magnetic resonance elastography (MRE) has been developed to noninvasively reconstruct mechanical properties for tissue and tissue-like materials over a frequency range of 10 ~200 Hz. In this work, low frequency (1~1.5 Hz) MRE activations were employed to estimate mechanical property distributions of simulated data and experimental phantoms. Nonlinear inversion (NLI) MRE algorithms based on viscoelastic and poroelastic material models were used to solve the inverse problems and recover images of the shear modulus and hydraulic conductivity. Data from a simulated phantom containing an inclusion with property contrast was carried out to study the feasibility of our low frequency actuated approach. To verify the stability of NLI algorithms for low frequency actuation, different levels of synthetic noise were added to the displacement data. Spatial distributions and property values were recovered well for noise level less than 5%. For the presented experimental phantom reconstructions with regularizations, the computed storage moduli from viscoelastic and poroelastic MRE gave similar results. Contrast was detected between inclusions and background in recovered hydraulic conductivity images. Results and findings confirm the feasibility of future in vivo neuroimaging examinations using natural cerebrovascular pulsations at cardiac frequencies, which can eliminate specialized equipment for high frequency actuation.

Syntheses, structures and catalytic properties of Evans-Showell-type polyoxometalate-based 3D metal-organic complexes constructed from the semi-rigid bis(pyridylformyl)piperazine ligand and transition metals.

Herein, two novel Evans-Showell-type polyoxometalate (POM)-based metal-organic complexes, namely, {[Cu(L)(H2O)3][Cu(L)0.5(H2O)][Cu(L)0.5(H2O)4][Co2Mo10H4O38]}·5H2O (1) and [(H2L)0.5]2{[Zn(L)0.5(H2O)4]2[Co2Mo10H4O38]}·2H2O (2) (L = N,N'-bis(3-pyridinecarboxamide)-piperazine), were hydrothermally synthesized using a semi-rigid bis-pyridyl-bis-amide ligand and structurally characterized via single-crystal X-ray diffraction, elemental analysis, IR spectroscopy, powder X-ray diffraction (PXRD) and thermogravimetric analyses (TGA). The single-crystal X-ray diffraction analysis shows that complex 1 is a 3D Evans-Showell-type POM-based metal-organic network. In complex 1, the 1D infinite double chain structure constructed from {{Cu[Co2Mo10H4O38]}4-L} units and the µ4-bridging L ligand are linked by quadrate Cu2L2 loops to form a 2D layer, which is further connected by µ2-bridging L ligands, forming a 3D (2,3,4)-connected metal-organic framework. Complex 2 displays 3D supramolecular networks based on 1D {[Co2Mo10H4O38]-Zn-L}n infinite chains, which are constructed from Evans-Showell-type polyoxoanions and µ2-bridging 3-bpfp ligands (via ligation of pyridyl nitrogen atoms). The different coordination modes of the POM polyanions, bis(pyridylformyl)piperazine ligands and ratios play key roles in the construction of the title complexes. Significantly, the ligand L shows a µ4-bridging coordination mode in complex 1, which is observed for the first time in a POM system. Compounds 1 and 2 represent the first examples of metal-organic complexes based on Evans-Showell-type polyoxoanion and transition metal-bis-pyrazine-bis-amide coordination complexes. The fluorescence properties of the title complexes are reported herein. In addition, the title complexes act as heterogeneous Lewis acid catalysts for the oxidation of benzyl alcohol, and can also be recovered and reused without any significant loss in activity. Significantly, compound 1 with a 3D metal-organic framework showed higher catalytic performance with 99.4% conversion and 98.8% selectivity for benzoic acid at 10 h than compound 2 with 3D supramolecular networks.

Evans-Showell-type polyoxometalate-based metal-organic complexes with novel 3D structures constructed from flexible bis-pyrazine-bis-amide ligands and copper metals: syntheses, structures, and fluorescence and catalytic properties.

Two new Evans-Showell-type polyoxometalate (POM)-based metal-organic complexes, namely {Cu3(L1)1.5(H2O)5[Co2Mo10H4O38]}·5H2O (1), {[Cu(L2)0.5(H2O)2]2[Co2Mo10H4O38]}·6H2O (2) (L1 = N,N'-bis(2-pyrazinecarboxamide)-1,4-butane, L2 = N,N'-bis(2-pyrazinecarboxamide)-1,6-hexane), were successfully synthesized and structurally characterized by single-crystal X-ray diffraction, elemental analysis, IR spectroscopy, powder X-ray diffraction (PXRD) and thermogravimetric analyses (TGA). In complex 1, the adjacent [Co2Mo10H4O38]6- polyoxoanions are linked by CuII ions to form a 1D Cu-[Co2Mo10H4O38]6- inorganic chain, which is further linked by ligand L1 and [Co2Mo10H4O38]6- polyoxoanions, forming a 3D metal-organic framework. In complex 2, the adjacent [Co2Mo10H4O38]6- polyoxoanions link the CuII ions to generate a 2D Cu-[Co2Mo10H4O38]6- inorganic layer, which is further connected with bidentate ligands L2 to obtain a 3D metal-organic framework. The structural diversities of compounds 1 and 2 showed that the spacer lengths of the flexible bis-pyrazine-bis-amide ligands play important roles in tuning the structures of the title complexes. Compounds 1 and 2 represent the first examples of 3D frameworks based on the Evans-Showell-type polyoxoanions and Cu-bis-pyrazine-bis-amide coordination complexes. Moreover, the ligand L1 was first successfully introduced into the POM system. The electrochemical and fluorescence properties of compounds 1 and 2 were discussed. As heterogeneous catalysts, compounds 1 and 2 have good catalytic activity for the oxidation of benzyl alcohol. Moreover, compound 2 has higher catalytic performance with 100% conversion and 98.0% selectivity for benzoic acid at 10 h. The difference in their catalytic performance may be mainly due to the difference of their structures. The catalysts can be recovered and reused without displaying any significant loss of activity.

Phantom evaluations of nonlinear inversion MR elastography.

This study evaluated non-linear inversion MRE (NLI-MRE) based on viscoelastic governing equations to determine its sensitivity to small, low contrast inclusions and interface changes in shear storage modulus and damping ratio. Reconstruction parameters identical to those used in recent in vivo MRE studies of mechanical property variations in small brain structures were applied. NLI-MRE was evaluated on four phantoms with contrast in stiffness and damping ratio. Image contrast to noise ratio was assessed as a function of inclusion diameter and property contrast, and edge and line spread functions were calculated as measures of imaging resolution. Phantoms were constructed from silicone, agar, and tofu materials. Reconstructed property estimates were compared with independent mechanical testing using dynamic mechanical analysis (DMA). The NLI-MRE technique detected inclusions as small as 8 mm with a stiffness contrast as low as 14%. Storage modulus images also showed an interface edge response distance of 11 mm. Damping ratio images distinguished inclusions with a diameter as small as 8 mm, and yielded an interface edge response distance of 10 mm. Property differences relative to DMA tests were in the 15%-20% range in most cases. In this study, NLI-MRE storage modulus estimates resolved the smallest inclusion with the lowest stiffness contrast, and spatial resolution of attenuation parameter images was quantified for the first time. These experiments and image quality metrics establish quantitative guidelines for the accuracy expected in vivo for MRE images of small brain structures, and provide a baseline for evaluating future improvements to the NLI-MRE pipeline.

A numerical framework for interstitial fluid pressure imaging in poroelastic MRE.

A numerical framework for interstitial fluid pressure imaging (IFPI) in biphasic materials is investigated based on three-dimensional nonlinear finite element poroelastic inversion. The objective is to reconstruct the time-harmonic pore-pressure field from tissue excitation in addition to the elastic parameters commonly associated with magnetic resonance elastography (MRE). The unknown pressure boundary conditions (PBCs) are estimated using the available full-volume displacement data from MRE. A subzone-based nonlinear inversion (NLI) technique is then used to update mechanical and hydrodynamical properties, given the appropriate subzone PBCs, by solving a pressure forward problem (PFP). The algorithm was evaluated on a single-inclusion phantom in which the elastic property and hydraulic conductivity images were recovered. Pressure field and material property estimates had spatial distributions reflecting their true counterparts in the phantom geometry with RMS errors around 20% for cases with 5% noise, but degraded significantly in both spatial distribution and property values for noise levels > 10%. When both shear moduli and hydraulic conductivity were estimated along with the pressure field, property value error rates were as high as 58%, 85% and 32% for the three quantities, respectively, and their spatial distributions were more distorted. Opportunities for improving the algorithm are discussed.

Gradient-Based Optimization for Poroelastic and Viscoelastic MR Elastography.

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized 'adjoint method' based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation.

Length scales and pinning of interfaces.

The pinning of interfaces and free discontinuities by defects and heterogeneities plays an important role in a variety of phenomena, including grain growth, martensitic phase transitions, ferroelectricity, dislocations and fracture. We explore the role of length scale on the pinning of interfaces and show that the width of the interface relative to the length scale of the heterogeneity can have a profound effect on the pinning behaviour, and ultimately on hysteresis. When the heterogeneity is large, the pinning is strong and can lead to stick-slip behaviour as predicted by various models in the literature. However, when the heterogeneity is small, we find that the interface may not be pinned in a significant manner. This shows that a potential route to making materials with low hysteresis is to introduce heterogeneities at a length scale that is small compared with the width of the phase boundary. Finally, the intermediate setting where the length scale of the heterogeneity is comparable to that of the interface width is characterized by complex interactions, thereby giving rise to a non-monotone relationship between the relative heterogeneity size and the critical depinning stress.

Insights into copper coordination in the EcoRI-DNA complex by ESR spectroscopy.

The EcoRI restriction endonuclease requires one divalent metal ion in each of two symmetrical and identical catalytic sites to catalyse double-strand DNA cleavage. Recently, we showed that Cu2+ binds outside the catalytic sites to a pair of new sites at H114 in each sub-unit, and inhibits Mg2+ -catalysed DNA cleavage. In order to provide more detailed structural information on this new metal ion binding site, we performed W-band (~94 GHz) and X-band (~9.5 GHz) electron spin resonance spectroscopic measurements on the EcoRI-DNA-(Cu2+ )2 complex. Cu2+ binding results in two distinct components with different gzz and Azz values. X-band electron spin echo envelope modulation results indicate that both components arise from a Cu2+ coordinated to histidine. This observation is further confirmed by the hyperfine sub-level correlation results. W-band electron nuclear double resonance spectra provide evidence for equatorial coordination of water molecules to the Cu2+ ions.