*Phys Rev E ; 101(1-1): 012128, 2020 Jan.*

##### RESUMO

The effect of boundary relaxation on pulsed field gradient (PFG) anomalous restricted diffusion is investigated in this paper. The PFG signal attenuation expressions of anomalous diffusion in plate, sphere, and cylinder are derived based on fractional calculus. In addition, approximate expressions for boundary relaxation induced short time signal attenuation under zero gradient field and boundary relaxation affected short time apparent diffusion coefficients are given in this paper. Unlike the exponential signal attenuation in normal diffusion, the PFG signal attenuation in anomalous diffusion with boundary relaxation is either a Mittag-Leffler-function-based attenuation or a stretched-exponential-function-based attenuation. The stretched exponential attenuations of all three structures clearly show the diffractive pattern. In contrast, only in the plate structure does the Mittag-Leffler-function-based attenuation display an obvious diffractive pattern. Additionally, anomalous diffusion with smaller time derivative order α has a weaker diffractive pattern and less signal attenuation. Moreover, the results demonstrate that boundary relaxation induced signal attenuation is significantly affected by the anomalous diffusion when no gradient field is applied. Meanwhile, the boundary relaxation significantly affects PFG signal attenuation of anomalous diffusion in the following ways: The boundary relaxation results in reduced radius from the minimum of the diffractive patterns, and it results in an increased apparent diffusion coefficient and decreased surfaces to volume ratio in varying the diffusion time experiment; the boundary relaxation also substantially affects the apparent diffusion coefficient of sphere structure in the variation of gradient experiment.

*Chem Commun (Camb) ; 56(11): 1681-1684, 2020 Feb 06.*

##### RESUMO

A functionalized dumbbell probe (FDP) based amplification method, termed as a cascading exponential amplification DNA machine (CEA-DNA machine), has been developed to autonomously accumulate single G-quadruplexes (SGQs) and twin-G-quadruplexes (TGQs) for robust fluorescence signal-on probing of miRNA-21.

##### Assuntos

DNA/química , MicroRNAs/sangue , Técnicas de Amplificação de Ácido Nucleico/métodos , Espectrometria de Fluorescência/métodos , Benzotiazóis/química , Técnicas Biossensoriais/métodos , Linhagem Celular Tumoral , DNA/genética , Sondas de DNA/química , Sondas de DNA/genética , Corantes Fluorescentes/química , Quadruplex G , Humanos , Sequências Repetidas Invertidas , Limite de Detecção , MicroRNAs/genética , Hibridização de Ácido Nucleico*J Chem Phys ; 145(19): 194202, 2016 Nov 21.*

##### RESUMO

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in nuclear magnetic resonance and magnetic resonance imaging. However, the interpretation of PFG anomalous diffusion is complicated. Moreover, the exact signal attenuation expression including the finite gradient pulse width effect has not been obtained based on fractional derivatives for PFG anomalous diffusion. In this paper, a new method, a Mainardi-Luchko-Pagnini (MLP) phase distribution approximation, is proposed to describe PFG fractional diffusion. MLP phase distribution is a non-Gaussian phase distribution. From the fractional derivative model, both the probability density function (PDF) of a spin in real space and the PDF of the spin's accumulating phase shift in virtual phase space are MLP distributions. The MLP phase distribution leads to a Mittag-Leffler function based PFG signal attenuation, which differs significantly from the exponential attenuation for normal diffusion and from the stretched exponential attenuation for fractional diffusion based on the fractal derivative model. A complete signal attenuation expression Eα(-Dfbα,ß*) including the finite gradient pulse width effect was obtained and it can handle all three types of PFG fractional diffusions. The result was also extended in a straightforward way to give a signal attenuation expression of fractional diffusion in PFG intramolecular multiple quantum coherence experiments, which has an nß dependence upon the order of coherence which is different from the familiar n2 dependence in normal diffusion. The results obtained in this study are in agreement with the results from the literature. The results in this paper provide a set of new, convenient approximation formalisms to interpret complex PFG fractional diffusion experiments.

##### Assuntos

Difusão , Imageamento por Ressonância Magnética , Espectroscopia de Ressonância Magnética , Modelos Teóricos*J Magn Reson ; 272: 25-36, 2016 11.*

##### RESUMO

Pulsed field gradient (PFG) NMR is a noninvasive tool to study anomalous diffusion, which exists widely in many systems such as in polymer or biological systems, in porous material, in single file structures and in fractal geometries. In a real system, the diffusion could be a restricted or a tortuous anomalous diffusion, rather than a free diffusion as the domains for fast and slow transport could coexist. Though there are signal attenuation expressions for free anomalous diffusion in literature, the signal attenuation formalisms for restricted anomalous diffusion is very limited, except for a restricted time-fractional diffusion within a plate reported recently. To better understand the PFG restricted fractional diffusion, in this paper, the PFG signal attenuation expressions were derived for three typical structures (plate, sphere, and cylinder) based on two models: fractal derivative model and fractional derivative model. These signal attenuation expressions include two parts, the time part Tn(t) and the space part Xn(r). Unlike normal diffusion, the time part Tn(t) in time-fractional diffusion can be either a Mittag-Leffler function from the fractional derivative model or a stretched exponential function from the fractal derivative model. However, provided the restricted normal diffusion and the restricted time-fractional diffusion are in an identical structure, they will have the same space part Xn(r) as both diffusions have the same space derivative parameter ß equaling 2, therefore, they should have similar diffractive patterns. The restricted general fractional diffusion within a plate is also investigated, which indicates that at a long time limit, the diffusion type is insignificant to the diffractive pattern that depends only on the structure and the gradient pulses. The expressions describing the time-dependent behaviors of apparent diffusion coefficient Df,app for restricted anomalous diffusion are also proposed in this paper. Both the short and long time-dependent behaviors of Df,app are distinct from that of normal diffusion. The general expressions for PFG restricted curvilinear diffusion of tube model were derived in a conventional way and its result agree with that obtained from the fractional derivative model with α equaling 1/2. Additionally, continuous-time random walk simulation was performed to give good support to the theoretical results. These theoretical results reported here will be valuable for researchers in analyzing PFG anomalous diffusion.

*J Magn Reson ; 269: 36-49, 2016 08.*

##### RESUMO

An instantaneous signal attenuation (ISA) method for analyzing pulsed field gradient (PFG) fractional diffusion (FD) has been developed, which is modified from the propagator approach developed in 2001 by Lin et al. for analyzing PFG normal diffusion. Both, the current ISA method and the propagator method have the same fundamental basis that the total signal attenuation (SA) is the accumulation of all the ISA, and the ISA is the average SA of the whole diffusion system at each moment. However, the manner of calculating ISA is different. Unlike the use of the instantaneous propagator in the propagator method, the current method directly calculates ISA as A(K(t'),t'+dt')/A(K(t'),t'), where A(K(t'),t'+dt') and A(K(t'),t') are the SA. This modification makes the current method applicable to PFG FD as the instantaneous propagator may not be obtainable in FD. The ISA method was applied to study PFG SA including the effect of finite gradient pulse widths (FGPW) for free FD, restricted FD and the FD affected by a non-homogeneous gradient field. The SA expressions were successfully obtained for all three types of free FDs while other current methods still have difficulty in obtaining all of them. The results from this method agree with reported results such as that obtained by the effective phase shift diffusion equation (EPSDE) method. The M-Wright phase distribution approximation was also used to derive an SA expression for time FD as a comparison, which agrees with ISA method. Additionally, the continuous-time random walk (CTRW) simulation was performed to simulate the SA of PFG FD, and the simulation results agree with the analytical results. Particularly, the CTRW simulation results give good support to the analytical results including FGPW effect for free FD and restricted time FD based on a fractional derivative model where there have been no corresponding theoretical reports to date. The theoretical SA expressions including FGPW obtained here such as [Formula: see text] may be applied to analyze PFG FD in polymer or biological systems with improved accuracy where SGP approximation cannot be satisfied. The method can perhaps provide new insight to FD MRI and hence benefit the development of diffusion biomarkers based on fractional derivative.

##### Assuntos

Algoritmos , Artefatos , Imagem de Difusão por Ressonância Magnética/métodos , Aumento da Imagem/métodos , Interpretação de Imagem Assistida por Computador/métodos , Reprodutibilidade dos Testes , Sensibilidade e Especificidade*Phys Rev E ; 93(3): 032152, 2016 Mar.*

##### RESUMO

We calculate the efficiency at the unified trade-off optimization criterion (the so-called maximum Ω criterion) representing a compromise between the useful energy and the lost energy of heat engines operating between two reservoirs at different temperatures and chemical potentials, and demonstrate that the linear coefficient 3/4 and quadratic coefficient 1/32 of the efficiency at maximum Ω are universal for heat engines under strong coupling and symmetry conditions. It is further proved that the conclusions obtained here also apply to the ecological optimization criterion.

*J Chem Phys ; 143(16): 164202, 2015 Oct 28.*

##### RESUMO

Inter-molecular multiple quantum coherence (iMQC) has important applications in NMR and MRI. However, the current theoretical methods still have some difficulties in analyzing the behavior of iMQC signal attenuation of pulsed field gradient diffusion experiments. In this paper, the iMQC diffusion experiments were analyzed by an effective phase shift diffusion equation (EPSDE) method, which is based on the idea that the accumulating phase shift (APS) can be viewed as the result of a diffusion process in virtual phase space (VPS) with effective diffusion coefficient K(2)(t) D (rad(2)/s) where K(t)=∫0 (t)Î³g(t')dt' is a wavenumber and D is the physical diffusion coefficient of the spin carrier in the real space. The term K(t(tot)) z1 needs to be added to the APS when K(t(tot)) is not zero. Most of the time, K(t(tot)) equals zero. However, in iMQC experiments, the condition K(t(tot)) equaling zero or being non-zero for each spin depends on the gradient pulse setting. The signal attenuations of these two types of iMQC, zero or non-zero K(t(tot)), were analyzed in detail for free and restricted diffusions, which shows that there are significant differences between these two types of iMQC. Particularly, if an apparent diffusion coefficient D(app) is used to analyze the signal attenuation, it equals nD for zero K(t(tot)) which agrees with current theoretical and experimental reports, while for non-zero K(t(tot)), it equals (2n - 1) D which agrees with experimental results from the literature; there are no similar theoretical results reported for comparison. The result that D(app) equals (2n - 1) D is important because the higher value of D(app) means that non-zero K(t(tot)) iMQC can potentially provide more contrast and measure slower diffusion rates than zero K(t(tot)) iMQC. The EPSDE method provides a new way to analyze iMQC diffusion experiments.

*J Magn Reson ; 259: 232-40, 2015 Oct.*

##### RESUMO

Pulsed field gradient (PFG) diffusion measurement has a lot of applications in NMR and MRI. Its analysis relies on the ability to obtain the signal attenuation expressions, which can be obtained by averaging over the accumulating phase shift distribution (APSD). However, current theoretical models are not robust or require approximations to get the APSD. Here, a new formalism, an effective phase shift diffusion (EPSD) equation method is presented to calculate the APSD directly. This is based on the idea that the gradient pulse effect on the change of the APSD can be viewed as a diffusion process in the virtual phase space (VPS). The EPSD has a diffusion coefficient, K(ß)(t)D rad(ß)/s(α), where α is time derivative order and ß is a space derivative order, respectively. The EPSD equations of VPS are built based on the diffusion equations of real space by replacing the diffusion coefficients and the coordinate system (from real space coordinate to virtual phase coordinate). Two different models, the fractal derivative model and the fractional derivative model from the literature were used to build the EPSD fractional diffusion equations. The APSD obtained from solving these EPSD equations were used to calculate the PFG signal attenuation. From the fractal derivative model the attenuation is exp(-Î³(ß)g(ß)Î´(ß)Df1t(α)), a stretched exponential function (SEF) attenuation, while from the fractional derivative model the attenuation is Eα,1(-Î³(ß)g(ß)Î´(ß)Df2t(α)), a Mittag-Leffler function (MLF) attenuation. The MLF attenuation can be reduced to SEF attenuation when α=1, and can be approximated as a SEF attenuation when the attenuation is small. Additionally, the effect of finite gradient pulse widths (FGPW) is calculated. From the fractal derivative model, the signal attenuation including FGPW effect is exp[ -Df1∫0(τ) K(ß)(t)dt(α)]. The results obtained in this study are in good agreement with the results in literature. Several expressions that describe signal attenuation have not been reported and that can be of great importance for the PFG experiments. This EPSD equation method provides a new, simple path to calculate signal attenuation of PFG NMR experiments.

*Phys Rev E Stat Nonlin Soft Matter Phys ; 91(5): 052118, 2015 May.*

##### RESUMO

Based on two capacitively coupled quantum dots in the Coulomb-blockade regime, a model of three-terminal quantum-dot refrigerators is proposed. With the help of the master equation, the transport properties of steady-state charge current and energy flow between two quantum dots and thermal reservoirs are revealed. It is expounded that such a structure can be used to construct a refrigerator by controlling the voltage bias and temperature ratio. The thermodynamic performance characteristics of the refrigerator are analyzed, including the cooling power, coefficient of performance (COP), maximum cooling power, and maximum COP. Moreover, the optimal regions of main performance parameters are determined. The influence of dissipative tunnel processes on the optimal performance is discussed in detail. Finally, the performance characteristics of the refrigerators operated in two different cases are compared.

*Magn Reson Med ; 71(3): 1082-92, 2014 Mar.*

##### RESUMO

PURPOSE: In this report, the feasibility of using blood as an agent for Chemical Exchange Saturation Transfer (CEST) effect is investigated. METHODS: The CEST effect of porcine blood samples was investigated on a 3.0 T MRI scanner using various power levels and on a 14.1 T NMR spectrometer. As a proof-of-concept that CEST can be used to image blood in vivo, the technique was applied in two locations of healthy human volunteers, namely, the femoral artery and the M1-segment of the middle cerebral artery. RESULTS: The blood sample experiments showed that maximum CEST Magnetization Transfer Ratio asymmetry (MTRasym) values of â¼ 12% were achieved, with likely contributions from multiple blood components. These findings were confirmed during the in vivo experiments where CEST signal of blood was clearly greater than surrounding muscular (2%) and brain tissue (3%). CONCLUSION: Ex vivo and in vivo results show that blood is a suitable CEST agent that generates sufficient CEST contrast relative to surrounding tissue.

##### Assuntos

Algoritmos , Análise Química do Sangue/métodos , Interpretação de Imagem Assistida por Computador/métodos , Angiografia por Ressonância Magnética/métodos , Artéria Cerebral Média/química , Adulto , Animais , Feminino , Humanos , Masculino , Reprodutibilidade dos Testes , Sensibilidade e Especificidade , Suínos , Adulto Jovem*Solid State Nucl Magn Reson ; 26(2): 87-98, 2004 Sep.*

##### RESUMO

Xenon-129 spectra in some heterogeneous polymer systems consist of two resonances which collapse to a single resonance as a function of temperature. Two different resonances arise from spatially separated, distinct sorption environments and spectral collapse occurs when xenon atoms diffuse from one environment to the other at a sufficiently fast rate. This exchange mechanism involves a distribution of time constants and a two domain lattice model is used to generate a realistic distribution of correlation times resulting from diffusion in a heterogeneous matrix. The distribution of correlation times is inhomogeneous in the sense that different xenon atoms would exchange between the two domains or environments with a variety of time constants and the resulting spectrum is a superposition of spectra associated with each of the time constants. To demonstrate the nature of exchange according to this model, diffusion out of a sphere is simulated which corresponds to a progressive saturation experiment used to determine the diffusion constant of xenon in polystyrene. Then the model is used to demonstrate the difference between homogeneous and heterogeneous spectral collapse in one- and two-dimensional examples. Lastly, the simulation model is used to interpret one- and two- dimensional xenon-129 line shape changes for xenon sorbed into poly(2,6-dimethyl-1,4-phenylene oxide) as a function of temperature. Two broad resonances are observed at low temperatures in this polymer corresponding to xenon-129 sorbed in high free volume and low free volume domains. Exchange between the two main resonances collapses the spectrum to a single peak at higher temperatures. Both the collapse in one dimension and exchange in two dimensions as a function of mixing time can be simulated using the distribution from the lattice model. An average domain size of 70 nm is estimated by combining the simulation of the exchange experiment with the results of a one-dimensional progressive saturation experiment. The size of the sites sorbing individual xenon atoms has been reported from positron annihilation lifetime spectroscopy as 1.4 nm for the high free volume sites and 0.3 nm for the low free volume sites. The domain size is more than an order of magnitude larger than the individual sorption site indicating that domains consist of many sites as assumed in the lattice model description.