Search

Acute thrombotic thrombocytopenic purpura (TTP) is a life‐threatening emergency and plasma exchange (PEX) is the initial treatment shown to reduce acute mortality.

Acute thrombotic thrombocytopenic purpura (TTP) is a life‐threatening emergency and plasma exchange (PEX) is the initial treatment shown to reduce acute mortality. To compare current practice in the United Kingdom (UK) against the standards set out in the 2012 British Society of Haematology guideline, and to better understand the issues affecting prompt initiation of PEX. The trainee research network HaemSTAR conducted a retrospective nationwide review of adults presenting to UK hospitals with a first episode of acute TTP. Data on 148 patients treated at 80 UK hospitals between 2014 and 2019 demonstrated that 64.8% of patients received PEX within 24 h. Diagnostic uncertainty was the most commonly cited reason for delayed treatment. Conversely, a shorter time to PEX occurred in patients who had red cell fragments or severe thrombocytopenia identified on their first complete blood count. Availability of on‐site PEX was associated with a greater proportion of patients receiving PEX within 8 h compared to patients transferred, but by 24 h there was no difference between the two groups and two‐thirds of all patients had received their first PEX. The mortality rate for patients that received PEX was 9.2%, with 27.8% of deaths linked to delayed treatment initiation. This is the first multi‐center evaluation of treatment delays in acute TTP and it will inform targeted pathways to improve prompt access to life‐saving intervention.

The porosity dependence of the formation factor for geologic media is examined from the perspective of universal scaling laws from percolation and effective medium theories. Over much of the range of observed porosity, the expected percolation scaling is observed, but the values of the numerical prefactor do not conform to the simple predictions from percolation theory. Combining effective medium and percolation theories produces a numerical prefactor whose value depends on both the threshold porosity and the porosity above which the formation factor crosses from percolation to effective medium scaling. This change allows extraction of a numerical value of the prefactor, which is reasonably close to experimental values. Subsequent evaluation of the porosity dependence of the formation factor shows that difficulties in prior comparisons of theory and experiment are largely removed when percolation scaling is allowed to transition to effective medium scaling far above the percolation threshold. A novel, theoretical porosity dependent formation factor model is developedOur theory is evaluated using a large database including 405 experimentsPorosity for switching scaling from percolation to effective medium theory is not universal

Tortuosity is a property of porous media that is invoked and used in the literature on hydrology, soil science, physics, and engineering. It has been defined in a variety of ways, one of which is a purely geometrical concept. In this study, we focused on the geometrical tortuosity and developed a model based on percolation theory and the finite‐size scaling approach. Our result, developed for porous media of any saturation, expresses the tortuosity as a power‐law function of the water content, the critical water content, and the system size. The model parameters include the fractal dimension of either the backbone (the flow‐carrying part of porous media) or the optimal path (for crossing the system between two opposite faces), which have clear physical meaning. The results may be combined with power laws, which percolation theory provides for the hydraulic or electrical conductivity, to develop the appropriate form that expresses the connectivity as a function of the water content of a pore space. Comparison with numerical simulations and experiments reported in the literature indicated that the model estimates the tortuosity accurately. Our model and results leads us to conclude that pore connectivity and tortuosity should be treated as two distinct properties and that significant uncertainty in results for the saturation dependence of the hydraulic conductivity is traceable to the confusion that mixes the two as a single concept.

We previously obtained exact solutions for the time dependence of the density operator in weakly coupled spin-½ ImSn systems during arbitrary RF irradiation of the I spins. The solutions for the density operator were written as explicit linear combinations of its product operator components (i.e., the operator basis set consisting of direct products of the I- and S-spin operators). Other solutions for the product-operator evolution of the density matrix have considered either evolution in the absence of RF irradiation or the case where the RF is sufficiently strong that J-coupling effects can be ignored. The present solutions therefore extend the range of applications that are accessible to the product-operator formalism and vector pictures of nuclear spin evolution. Here, we derive the solutions for an IS system in detail to illustrate the simplicity of the formalism and supplement our previous, but more general, abstract treatment of the subject. We then outline how the formalism is applied to the ImSn case. We also briefly discuss the rigorous vector picture that can be associated with the states of the system at each time. The solutions provide new insight into the combined effects of RF irradiation and J-coupling. Applications include (1) novel methods for calibrating an RF channel for insensitive I spins by observing large signals from multiple quantum coherences with the S-spin channel, and (2) new RF pulses for achieving selective coherence transfer. © 2002 Wiley Periodicals, Inc. Concepts Magn Reson 14: 287–307, 2002.

A comprehensive survey is provided of the analytical expressions for the orthogonal product operator states arising from any initial state of an IS J-coupled spin system during arbitrary RF irradiation of one spin. These equations exactly characterize the effect of Jcoupling during the application of the RF field. The survey differentiates two kinds of spin rotation, classical and nonclassical, where the second kind comprises any interconversion that includes the transverse two-spin coherence states, 2SyIxor 2SyIy, as initial, transient, or final states, and the first kind comprises all other rotations. Classical rotations are defined as linear rotations of the nuclear spin magnetization vectors around effective fields and there is an exact correspondence between the resulting vector model and the quantum mechanical (QM) equations at all RF field strengths. The effect of scalar coupling can be neglected for B1> 5J. Nonclassical rotations are nonlinear in time for a constant RF field. At high field (B1> 50J), the effect of Jmodulation is negligible, and the rotation of magnetizations is classical to a very good approximation. At intermediate strengths (5J< B1< 50J), a semi-classical vector model of I-spin irradiation is applicable in which the J-coupled precession of the S spins is determined from a reduced coupling constant, but the effect of the S spins on the I spins is ignored (this model has previously been used to determine the effect of coupling during adiabatic pulses). At lower powers, the exact QM-derived equations must be used for nonclassical rotations, but continuous pictorial descriptions of the rotation of magnetizations determined from the vector sum of the product operator states are helpful in designing novel NMR applications. At all powers it is proven that the instantaneous reduced coupling constant acting on the S spins is Jcosφ, where φ is the polar angle of the I-spin magnetizations, thus establishing the central tenet of the semi-classical model applicable at moderate power. Several spinstate transformations that combine the effects of RF and scalar coupling to produce the overall rotation can be generated in 100% yield using low power irradiation. Analogous transformations are also available using classical rotations and, in combination with their nonclassical counterparts, form a general class of frequency-selective pulses that we call Jpulses. Any combination of a 90° pulse and a consecutive (2J)−1delay period can be replaced with a Jpulse, and some initial approaches to designing shaped Jpulses with improved offset profiles are explored.

Exact solutions for the effect of time-independent RF pulses on any initial configuration of an IS J-coupled system demonstrate that on-resonance CW decoupling yields signals whose frequency depends on RF field strength and homogeneity. These signals are enhanced starting with “undetectable” antiphase and multiple quantum coherences, which can also produce centerband intensity to mimic the signal from decoupled Sx. Conversely, these coherences can be generated from Sxusing a low-power pulse, B1= J/2, of length (2J)−1, dubbed a “90Jpulse” since it is the selective equivalent of {(2J)−1–90[I]}. Utilizing 90Jpulses, new characterization-of-decoupler (COD) pulse sequences can determine the performance of an insensitive I-spin channel by observing large signals from either antiphase or multiple quantum coherences with the S-spin channel, allowing, in minutes rather than hours: (i) frequency calibration to an accuracy of 0.1 Hz; (ii) measurement of RF amplitudes over a 500-fold variation; and (iii) mapping of RF homogeneity along the sample axis with a single 1D B1spectrum. These 90Jcoherence transfer pulses are of potential general use for selective spectroscopy.

In this article, we consider the evolution of weakly coupled ImSnsystems of spin-12nuclei during arbitrary RF irradiation of the I spins. Exact solutions are presented for the time dependence of the density operator in terms of its constituent product operator components for a complete set of initial states derived from polarization of either the I or the S spin. The solutions extend the range of applications that are accessible to the product operator formalism and its associated vector picture of nuclear spin evolution. This marriage of quantum mechanics and a literal vector description of spin dynamics during RF irradiation supports physical intuition and has led to simple pulses for selective coherence transfer, among other new applications. The evolution of initial states that are free of transverse S-spin components can be described by classical precession of the I-spin components about effective fields defined by the interaction between the coupling and RF fields. Although there is no analogue involving classical rotations for the evolution of initial states composed of Sxor Sy, a vector description is still possible, and the solutions completely characterize the nature of J-coupling modulation during RF pulses. We emphasize the Cartesian product operator basis in the present treatment, but the solutions are readily obtained in any other basis that might prove suitable in analyzing an experiment. For a system of Ncoupled spins, standard exact methods involving diagonalization and multiplication of the 2N× 2Nmatrices that represent the system require on the order of (2N)3operations to calculate the system response to a general RF waveform at each point in the time domain. By contrast, the efficiency of the present method scales linearly with the number of spins. Since the formalism presented also accommodates the absence of either RF irradiation or the coupling, the solutions provide an efficient means of general pulse sequence simulation, encompassing any combination of arbitrary RF waveforms, delays, and coherence gradients.

Exact product operator solutions have been obtained for the evolution of weakly coupled spin-12ImSnsystems during arbitrary RF irradiation of one spin. These solutions, which completely characterize the nature of J-coupling modulation during RF pulses, show that significant exchange occurs between single-spin magnetization and two-spin product operator states when the RF field strength is comparable to the coupling. In particular, a long (tp= [2J]−1s), low-power (B1= J/2 Hz), constant amplitude pulse applied on resonance to one spin in an IS system completely interconverts the spinstates Sz↔ 2SxIzand Sx↔ 2SzIzwhen the RF is applied to the S spins, and interconverts Sx↔ 2SyIyin 100% yield when the RF is applied to the I spins. Thus, these “Jpulses,” which select a bandwidth approximately equal to JHz, may replace any combination of a (2J)−1delay period and a consecutive hard 90° pulse in any polarization transfer or multiple quantum sequence. Although these rectangular pulses are highly frequency selective, in general they increase the replaced (2J)−1period by only a modest 40%, a time saving of a factor of 5 compared to existing pulses exhibiting the same selectivity. In favorable cases, there is no increase in duration of a pulse sequence using a particular type of Jpulse, the 90Jvariety, which accomplishes the third spin state transformation listed above. Jpulses will be advantageous for systems subject to rapid signal loss from relaxation and more generally for the enhanced operation of pulse sequences via the use of Jmodulation during RF irradiation.

RF pulse sequences applied to IS spin systems may produce substantial transverse antiphase S magnetization coupled to antiphase I magnetization, just prior to detection of the S signal, for samples containing a range ofJcoupling constants, or when pulse sequence delays are misset from ideal values. This magnetization is generally considered to be unobservable. Adiabatic decoupling on the I spins during signal detection efficiently converts this magnetization to observable S signal in the form of sidebands which we dub “coherence sidebands.” Three single-transient pulsed-field-gradient methods are described for eliminating these unwanted sidebands. The techniques are applicable to1H-detected13C-decoupled experiments on spectrometers operating at a1H frequency of up to 2 GHz.

To provide the most efficient conditions for spin decoupling with least RF power, master calibration curves are provided for the maximum centerband amplitude, and the minimum amplitude for the largest cycling sideband, resulting from STUD+ adiabatic decoupling applied during a single free induction decay. The principal curve is defined as a function of the four most critical experimental input parameters: the maximum amplitude of the RF field,RFmax, the length of the sech/tanh pulse,Tp, the extent of the frequency sweep,bwdth,and the coupling constant,Jo. Less critical parameters, the effective (or actual) decoupled bandwidth,bweff, and the sech/tanh truncation factor, β, which become more important asbwdthis decreased, are calibrated in separate curves. The relative importance of nine additional factors in determining optimal decoupling performance in a single transient are considered. Specific parameters for efficient adiabatic decoupling can be determined via a set of four equations which will be most useful for13C decoupling, covering the range of one-bond13C1H coupling constants from 125 to 225 Hz, and decoupled bandwidths of 7 to 100 kHz, with a bandwidth of 100 kHz being the requirement for a 2 GHz spectrometer. The four equations are derived from a recent vector model of adiabatic decoupling, and experiment, supported by computer simulations. The vector model predicts an inverse linear relation between the centerband and maximum sideband amplitudes, and it predicts a simple parabolic relationship between maximum sideband amplitude and the productJoTp. The ratiobwdth/(RFmax)2can be viewed as a characteristic time scale, τc, affecting sideband levels, with τc≈Tpgiving the most efficient STUD+ decoupling, as suggested by the adiabatic condition. Functional relationships betweenbwdthand less critical parameters,bweffand β, for efficient decoupling can be derived from Bloch-equation calculations of the inversion profile for a single sech/tanh pulse. Residual splitting of the centerband, normally associated with incomplete or inefficient decoupling, is not seen in sech/tanh decoupling and therefore cannot be used as a measure of adiabatic decoupling efficiency. The calibrated experimental performance levels achieved in this study are within 20% of theoretical performance levels derived previously for ideal sech/tanh decoupling at high power, indicating a small scope for further improvement at practical RF power levels. The optimization procedures employed here will be generally applicable to any good combination of adiabatic inversion pulse and phase cycle.

Most states provide public technical assistance to help private landowners manage their forests. This article summarizes the results of a case study evaluating the public forestry assistance program in Georgia. Forest harvesting practices made by private landowners who received public forestry assistance were compared with those who did not receive any assistance when making a timber sale and harvest. Assisted landowners generally had greater returns from harvests, which could be imputed to yield large private, social, and program benefit cost ratios.

Experimental calibration of the amplitude of sidebands resulting from STUD decoupling over a range of decoupled bandwidths from 2 to 120 kHz shows that sideband amplitude depends on the length of each single sech/tanh pulse,Tp, and the bandwidth divided by the square of the maximum RF amplitude during the pulse, bwdth/(RFmax)2. Plots of sideband amplitude versus bwdth/(RFmax)2are independent of bandwidth and so provide convenient calibration curves enabling choice ofTp. Such calibration curves will vary modestly between NMR probes because of the differing homogeneity of the RF field produced by the probe across the sample. The dependence on bwdth/(RFmax)2arises from the inversion efficiency of a single sech/tanh pulse. This dependence corresponds to the principle that the optimal RF power required for STUD decoupling is linearly proportional to the chosen decoupled bandwidth. This behavior, which is common to adiabatic decoupling methods, is different from composite-pulse decoupling schemes where chosen bandwidths and corresponding optimal RF power settings are more limited, and effective bandwidths are proportional to the applied RF amplitude rather than RF power. The STUD method achieves the widest effective decoupled bandwidths of any broadband technique to date when decoupling schemes are compared at the same average power. This is particularly relevant to applications where sample heating must be minimized. Additional criteria for good decoupling performance are considered in further detail. The accurate measurement of sideband amplitudes is shown to provide a convenient means for evaluating the efficiency of different decoupling schemes. Adiabatic decoupling methods are especially interesting since, in contrast to composite-pulse methods, the RF amplitude and pulse length can be varied separately, providing additional opportunity for comparison with theoretical models of decoupling. In particular, exceptions to a frequently cited condition for minimizing sideband intensity,TcJ<< 1, whereTcis the cycle time to return the irradiated spins to their initial orientation, are discussed.

A vector model of adiabatic decoupling is enunciated for an IS-coupled system of two spin-12heteronuclei in the high-power limit of ideal adiabatic pulses. The observed S-spin magnetization evolves according to a time-dependent coupling that scales as thezcomponent of an I-spin vector which evolves due to the applied decoupling irradiation. Simple analytical expressions are derived both on and off resonance for the reduced coupling during an ideal sech/tanh inversion pulse and for the resulting signal when either in-phase or antiphase magnetization is present at the start of decoupling. The resulting model allows one to readily envision decoupling experiments, make accurate estimates of sideband intensity, and assess the relative performance of different decoupling schemes. The utility of the model is further demonstrated by applying it to several recently proposed methods for reducing sidebands. In the limit of ideal adiabatic pulses, the predictions of the vector model are almost identical to those of quantum mechanics. At the lower RF power levels used in practical adiabatic decoupling applications, where the pulses are no longer perfectly adiabatic, phase cycles are employed to achieve performance that approximates the ideal limits derived here, so the vector model is more generally applicable, as well. These limits establish standards for future determination of the most efficient parameters for practical applications of broadband adiabatic decoupling in a single transient.

When an optical imaging system is treated as a linear system, for incoherently illuminated objects, a statistically homogeneous, isotropic, random medium placed between the object and the imaging system multiplies the free-space transfer function of the optical system by a correction factor. If a medium having a Gaussian-correlated refractive index is assumed, then the correction factor for an on-axis quasimonochromatic point source has the form a+b erf x/x for propagation distances that are in the near field of the correlation interval of the medium. This form is found by using the first Born approximation to the two coupled wave equations satisfied by a mutual coherence function. The ensemble-averaged effect of imaging through a random medium is that the medium acts as a low-pass filter, decreasing the resolution of the imaging system.

By assuming the random, time-varying boundary conditions for the scalar wave equation to be ergodic, we can associate with the time-varying boundary conditions an ensemble of strictly monochromatic boundary conditions. Formally solving and comparing the solutions for each type of boundary condition, we conclude that the time-averaged and ensemble-averaged powers (squares of the field) are the same at all points where the path difference to any two points on the boundary is small compared to c/Δν, where c is the free-space speed of light and Δν is the frequency spread of the time-varying boundary conditions. That is, if the boundary conditions are ergodic, the solutions are ergodic.

By assuming the random, time-varying boundary conditions for the scalar wave equation to be ergodic, we can associate with the time-varying boundary conditions an ensemble of strictly monochromatic boundary conditions. Formally solving and comparing the solutions for each type of boundary condition, we conclude that the time-averaged and ensemble-averaged powers (squares of the field) are the same at all points where the path difference to any two points on the boundary is small compared to c/Δv, where c is the free-space speed of light and Δv is the frequency spread of the time-varying boundary conditions. That is, if the boundary conditions are ergodic, the solutions are ergodic.

Using the formulation of coherence theory as introduced by Wolf, the diffraction of partially coherent light is discussed. The mutual coherence function and the intensity distribution are computed for a plane slit illuminated by coherent, partially coherent and incoherent light. The results are plotted and discussed.

A new algorithm is presented that provides separate water, fat, and B0images utilizing the in‐phase and opposed‐phase acquisitions of the two‐point Dixon (2PD) method. The accuracy of the extended method (E2PD) compares favorably with the three‐point Dixon (3PD) method, and the acquisition requires 2/3 the 3PD scan time. Slightly increased mismapping may occur in pixels containing an admixture of water and fat due to reduced SNR in the B0field map compared with the 3PD method.

When an optical imaging system is treated as a linear system, for incoherently illuminated objects, a statistically homogeneous, isotropic, random medium placed between the object and the imaging system multiplies the free-space transfer function of the optical system by a correction factor. If a medium having a Gaussian-correlated refractive index is assumed, then the correction factor for an on-axis quasimonochromatic point source has the form a+b erf x/x for propagation distances that are in the near field of the correlation interval of the medium. This form is found by using the first Born approximation to the two coupled wave equations satisfied by a mutual coherence function. The ensemble-averaged effect of imaging through a random medium is that the medium acts as a low-pass filter, decreasing the resolution of the imaging system.

The characteristics of grain boundary motion and evolution are of fundamental importance in material science. Optical microscopy is used to analyse grain boundary fluctuations in two-dimensional colloidal crystals. Colloidal systems are particles (colloids) on the order of 1µm dispersed in a solvent where they display rich phase behaviour of colloidal 'crystal', liquid' and 'gas' phases. They are widely used as a model system to study many fundamental issues in condensed matter physics and statistical mechanics. The intrinsic slowness and increased length scales of colloidal systems make them an excellent model system to study grain boundaries as an analogy to atomic systems. Static and dynamic correlation functions are compared with capillary wave theory to calculate the grain boundary mobility and stiffness. These fundamental properties of grain boundaries determine the kinetics of curvature-driven grain growth.

The lack of a method to isolate very hydrophilic 3-hydroxypyridin-4-ones (HPs) from blood has prevented determination of their pharmacokinetics. The objective of this study is to develop a method to quantitate these compounds. A simple sample preparation method coupled with high-performance liquid chromatography is used to quantitate 1-[ethan-1-ol]-2-methyl-3-hydroxypyridin-4-one, a very hydrophilic HP, in plasma. Plasma proteins are precipitated by trichloroacetic acid. The baseline file subtraction method is used to improve the resolution of this HP in the presence of interfering chromatographic peaks that could not be resolved from the HP by the methods investigated. The method is used to determine the pharmacokinetics of this HP in rabbits. The precision of the pharmacokinetic results is comparable or better than the results obtained from seven more lipophilic HPs that were separated by a published method. The new method is slightly modified and used in a study of the pharmacokinetics of this HP in the rat, and precision is comparable with results obtained with two more lipophilic HPs determined by the published method. Baseline file subtraction is useful when other methods cannot be used to adequately resolve a hydrophilic analyte from coeluting interfering substances.