Bloch Model Research Articles

T1234: A distortion-matched structural scan solution to misregistration of high resolution fMRI data.

High-resolution fMRI at 7T is challenged by suboptimal alignment quality between functional data and structural scans. This study aims to develop a rapid acquisition method that provides distortion-matched, artifact-mitigated structural reference data. We introduce an efficient sequence protocol termed T1234, which offers adjustable distortions. This approach involves a T1-weighted 2-inversion 3D-EPI sequence with four spatial encoding directions optimized for high-resolution fMRI. A forward Bloch model was used for T1 quantification and protocol optimization. Twenty participants were scanned at 7T using both structural and functional protocols to evaluate the utility of T1234. Results from two protocols are presented. A fast distortion-free protocol reliably produced whole-brain segmentations at 0.8mm isotropic resolution within 3:00-3:40 minutes. It demonstrates robustness across sessions, participants, and three different 7T SIEMENS scanners. For a protocol with geometric distortions that matched functional data, T1234 facilitates layer-specific fMRI signal analysis with enhanced laminar precision. This structural mapping approach enables precise registration with fMRI data. T1234 has been successfully implemented, validated, and tested, and is now available to users at our center and at over 50 centers worldwide.

Analysis and numerical simulation of fractional Bloch model arising in magnetic resonance imaging using novel iterative technique

Analysis and numerical simulation of fractional Bloch model arising in magnetic resonance imaging using novel iterative technique

Evaluation of lithium as a tritium storage medium for betavoltaics

Lithium foils were demonstrated to absorb surrogate protium for tritium-powered betavoltaics. 20 μm thick lithium foils were hole-punched from a ribbon of electrodeposited lithium on copper foil. The lithium foils were loaded with hydrogen in a custom Sievert apparatus where the pressure drop showed full hydriding at a hydrogen pressure of 2 bar and at all loading temperatures above the lithium melting point at 190, 200, 225, 250, and 300. Lithium hydride formation was confirmed with Raman spectroscopy after hydrogen loading. The kinetics of experimental hydride formation was compared to the diffusion-limited Mintz–Bloch model. While the Mintz–Bloch model showed good fit with the experimental loadings, the model overpredicted the loading kinetics starting at 250 °C and at higher temperatures. The overprediction was either caused by lithium hydride outgassing due to some reduction with some residual lithium hydroxide created from brief air exposure when sealing the lithium in the reactor or a transition from diffusion-limited hydride growth to surface or metal–hydride interface-limited hydride growth.

Rapid quantitative magnetization transfer imaging: Utilizing the hybrid state and the generalized Bloch model.

To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model parameters. We combine two recently proposed models in a Bloch-McConnell equation: the dynamics of the free spin pool are confined to the hybrid state, and the dynamics of the semi-solid spin pool are described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three qMT parameters while accounting for all eight parameters of the two-pool model. We sparsely sample each time frame along this spin dynamics with a three-dimensional radial koosh-ball trajectory, reconstruct the data with subspace modeling, and fit the qMT model with a neural network for computational efficiency. We extracted qMT parameter maps of the whole brain with an effective resolution of 1.24 mm from a 12.6-min scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi-solid spin pool and longer relaxation times, consistent with previous reports. The encoding power of the hybrid state, combined with regularized image reconstruction, and the accuracy of the generalized Bloch model provide an excellent basis for efficient quantitative magnetization transfer imaging with few constraints on model parameters.

Fractal Bloch model to characterize stretched magnetization relaxation in magnetic resonance imaging

This study proposes a fractal Bloch model to describe the stretched magnetization relaxation in magnetic resonance imaging (MRI). The fractal Bloch model extends the relaxation terms and preserves the linear Larmor precession terms under a constant magnetic field. The solutions of the fractal Bloch model have the form of stretched exponential and converge to the exponential form for the classical Bloch equation when the orders of the fractal derivative α=1, and β=1. The results show that the damped oscillations in Mx(t) or My(t) have a faster decay at short times, and slower decay at long times with the increasing values of α. The relaxation of Mz(t) with the stretched-exponential form increases more quickly than the exponential case at first, but then converges more slowly to the equilibrium magnetization, which needs a longer time to return the equilibrium in the cases of smaller order β. The fractal Bloch model is verified to characterize the signal decays in rat brain and bovine nasal cartilage. The fitting results show that the fractal Bloch model is effective to describe the stretched magnetization relaxation in MRI data. Thus, the fractal derivative is an alternative tool to use to understand MRI in complex systems, and its order can serve as an index to distinguish different relaxation processes in magnetization.

Strang splitting schemes forN-level Bloch models

In this paper, we define a splitting scheme for the N-level Bloch model which makes use of exact numerical solutions of sub-equations. These exact solutions involve matrix exponentials which we want to avoid to calculate at each time-step. The resulting scheme is nonstandard and preserves qualitative properties of the Bloch equations. We explore and compare numerically multiple ways to implement it and in particular take into account the specific structure of the Bloch equations.

Self-consistent Maxwell–Bloch model for high-order harmonic generation in nanostructured semiconductors

In pursuit of efficient high-order harmonic conversion in semiconductor devices, modeling insights into the complex interplay among ultrafast microscopic electron–hole dynamics, nonlinear pulse propagation, and field confinement in nanostructured materials are urgently needed. Here, a self-consistent approach coupling semiconductor Bloch and Maxwell equations is applied to compute transmission and reflection high-order harmonic spectra for finite slab and sub-wavelength nanoparticle geometries. An increase in the generated high harmonics by several orders of magnitude is predicted for gallium arsenide nanoparticles with a size maximizing the magnetic dipole resonance. Serving as a conceptual and predictive tool for ultrafast spatiotemporal nonlinear optical responses of nanostructures with arbitrary geometry, our approach is anticipated to deliver new strategies for optimal harmonic manipulation in semiconductor metadevices.

The application of the distributed-order time fractional Bloch model to magnetic resonance imaging

It is now well known that the magnetic resonance imaging (MRI) signal decay deviates from the classical mono-exponential relaxation. This deviation is referred to in the literature as anomalous relaxation. The modelling of this anomalous relaxation can provide a better understanding of MRI magnetization. The purpose of this work is to investigate the utility of the distributed-order time fractional Bloch equations to describe anomalous relaxation processes in human brain MRI data. Two choices of continuous distribution weight functions, which are parameterised by their mean μ and standard deviation σ, are studied to investigate their impact on the model solution behaviour. An implicit numerical method implemented on a graded mesh is proposed to solve the model and the stability and convergence analysis are presented. We also derive semi-analytical solutions of the fully coupled Bloch equations using the Laplace transform technique to assess the accuracy of the numerical scheme. Furthermore, three different voxel models of continuous distribution weight functions, namely a single continuous probability distribution (model 1), two distinct continuous probability distributions (model 2) and a mixture of two continuous probability distributions (model 3), are applied to the in vivo human brain MRI data, and a feasible and reliable parameter estimation method based on a modified hybrid Nelder-Mead simplex search and particle swarm optimization is presented to perform the voxel-level temporal fitting of the MRI data. The application of these distributed-order time fractional Bloch models highlights the validity of the proposed models, and based on the mean square error we conclude that models 2 and 3 might be more suitable than model 1 to characterize anomalous relaxation processes in human brain MRI data.

Optical pump assisted broadband terahertz frequency comb

A broadband terahertz (THz) frequency comb assisted by an optical pump in THz quantum cascade lasers (QCLs) is investigated theoretically and numerically through a Maxwell–Bloch model combined with the coupled wave theory. When an optical pump is injected into the laser cavity with dispersion, the intrinsic four-wave-mixing nonlinear process becomes not only an important elementary phase-locking mechanism during the mode proliferating process, but also the bandwidth of the frequency comb is increased and the power is amplified through the nonlinear parametric process. The relative shift between the frequency of the optical pump and the zero-dispersion frequency of THz QCLs tremendously affects the conversion efficiency of the nonlinear parametric process. The simulation results show that appropriately optical pumping could assist in generating the broadband THz frequency comb with over 1 THz and more than 80 lines, which may open many potential applications in designing and optimizing high resolution THz spectroscopy sources.

Generalized Bloch model: A theory for pulsed magnetization transfer.

The paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization transfer (MT) to spins of nuclei in water. Like quantum-mechanical descriptions of spin dynamics and like the original Bloch equations, but unlike existing MT models, the proposed model is based on the algebra of angular momentum in the sense that it explicitly models the rotations induced by radiofrequency (RF) pulses. It generalizes the original Bloch model to non-exponential decays, which are, for example, observed for semi-solid spin pools. The combination of rotations with non-exponential decays is facilitated by describing the latter as Green's functions, comprised in an integro-differential equation. Our model describes the data of an inversion-recovery magnetization-transfer experiment with varying durations of the inversion pulse substantially better than established models. We made this observation for all measured data, but in particular for pulse durations smaller than 300μs. Furthermore, we provide a linear approximation of the generalized Bloch model that reduces the simulation time by approximately a factor 15,000, enabling simulation of the spin dynamics caused by a rectangular RF-pulse in roughly 2μs. The proposed theory unifies the original Bloch model, Henkelman's steady-state theory for MT, and the commonly assumed rotation induced by hard pulses (i.e., strong and infinitesimally short applications of RF-fields) and describes experimental data better than previous models.

Fast and accurate modeling of transient-state, gradient-spoiled sequences by recurrent neural networks.

Fast and accurate modeling of MR signal responses are typically required for various quantitative MRI applications, such as MR fingerprinting. This work uses a new extended phase graph (EPG)‐Bloch model for accurate simulation of transient‐state, gradient‐spoiled MR sequences, and proposes a recurrent neural network (RNN) as a fast surrogate of the EPG‐Bloch model for computing large‐scale MR signals and derivatives. The computational efficiency of the RNN model is demonstrated by comparisons with other existing models, showing one to three orders of acceleration compared with the latest GPU‐accelerated, open‐source EPG package. By using numerical and in vivo brain data, two used cases, namely, MRF dictionary generation and optimal experimental design, are also provided. Results show that the RNN surrogate model can be efficiently used for computing large‐scale dictionaries of transient‐state signals and derivatives within tens of seconds, resulting in several orders of magnitude acceleration with respect to state‐of‐the‐art implementations. The practical application of transient‐state quantitative techniques can therefore be substantially facilitated.

National myths and rebounding violence

AbstractThe article takes up the sacrificial theory of national myths presented by Steven J. Mock and discloses its further potential for understanding the symbolic structures of nationalism. While Mock builds mainly on a Girardian reinterpretation of Freud, I try to show that even more interesting results may be obtained by using Maurice Bloch's theory of ritual symbolism. The advantage of Bloch's model is threefold. (1) It discloses further interesting aspects of the sacrificial symbolism in national myths not noted by Mock. I illustrate some of these by a detailed analysis of the Czech national myth. (2) Bloch's model allows us to trace the sacrificial pattern not just in myths of the modern awakening of the nation but in myths concerning present‐day political events as well. As an example, I analyse symbols of defeat in several myths of Czech 20th‐century political leaders. (3) Bloch's model is more complex and thus allows us to understand different types of national myths than those featuring symbolism of defeat. As an example, I discuss imperial nationalism, which Mock considers as one of the exceptions to his theory, and I also use Bloch to throw interesting light on the distinction between “civic” and “ethnic” nationalism.

New Aspects of Bloch Model Associated with Fractal Fractional Derivatives

Abstract To model complex real world problems, the novel concept of non-local fractal-fractional differential and integral operators with two orders (fractional order and fractal dimension) have been used as mathematical tools in contrast to classical derivatives and integrals. In this paper, we consider Bloch equations with fractal-fractional derivatives. We find the general solutions for components of magnetization ℳ = (Mu , Mv , Mw ) by using descritization and Lagrange's two step polynomial interpolation. We analyze the model with three different kernels namely power function, exponential decay function and Mittag-Leffler type function. We provide graphical behaviour of magnetization components ℳ = (Mu , Mv , Mw ) on different orders. The examination of Bloch equations with fractal-fractional derivatives show new aspects of Bloch equations.

New aspects of fractional Bloch model associated with composite fractional derivative

This paper studies a fractional Bloch equation pertaining to Hilfer fractional operator. Bloch equation is broadly applied in physics, chemistry, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and many more. The sumudu transform technique is applied to obtain the analytic solutions for nuclear magnetizationM= (Mx,My,Mz). The general solution of nuclear magnetizationMis shown in the terms of Mittag-Leffler (ML) type function. The influence of order and type of Hilfer fractional operator on nuclear magnetizationMis demonstrated in graphical form. The study of Bloch equation with composite fractional derivative reveals the new features of Bloch equation. The discussed fractional Bloch model provides crucial and applicable results to introduce novel information in scientific and technological fields.

Propagation of electric field generated by periodic pumping in a stable medium of two-level atoms of the Maxwell–Bloch model

We consider the problem of the propagation of an electric field generated by periodic pumping in a stable medium of two-level atoms as the mixed problem for the Maxwell–Bloch equations without spectrum broadening. An approach to the study of such a problem is proposed. We use the inverse scattering transform method in the form of the matrix Riemann–Hilbert (RH) problem, using simultaneous spectral analysis of both the Lax equations. The proposed matrix RH problem solves the problem of the propagation of a sinusoidal signal in an unperturbed stable medium (attenuator). It is proved that this RH problem provides the causality principle for the region t < x, and for the region of the light cone, 0 < x < t allows us to find the asymptotics of the transmitted signal. First, we study the asymptotics of the RH problem for large times, and then, we obtain asymptotic formulas for the mixed problem solution of the Maxwell–Bloch equations when the attenuator is long enough. Three sectors are obtained in the light cone where the asymptotics have essentially different behaviors.

Q-homotopy analysis method for fractional Bloch model arising in nuclear magnetic resonance via the Laplace transform

In this article, the numerical solution of fractional-order Bloch equations in MRI is obtained using q-homotopy analysis transform method (q-HATM). The results are compared with those from the existing methods and the exact solution. The results for fractional values of time derivative are discussed using figures and tables. Figures are made using Maple package. The provided examples illustrate the accuracy and competency of the q-HATM.

The numerical investigation of colliding optical solitons as an all-optical-gate using the method of Lines

The bidirectional propagation and collision of counter-propagating optical solitons in a two-level resonant medium is analyzed. For sufficiently short duration of the pulses and sufficiently high power levels, self-induced transparency allows the pulses to propagate without losses at anomalously low velocities. Here, we use an extended semiclassical approach, called Maxwell–Bloch model. The quantization of the electromagnetic field is neglected, however, a full quantum mechanical formulation is used to describe the behavior of the matter. The numerical simulations are performed by using the method of lines. For improved accuracy, spline interpolation of the fields is introduced. Results are presented to demonstrate the use of soliton collision for all-optical switching, in particular, as OR- and XOR-gates.

Attosecond x-ray transient absorption in condensed-matter: a core-state-resolved Bloch model

Attosecond transient absorption is an ultrafast technique that has opened the possibility to study electron dynamics in condensed matter systems at its natural timescale. The extension to the x-ray regime permits one to use this powerful technique in combination with the characteristic element specificity of x-ray spectroscopy. At these timescales, the coherent effects of the electron transport are essential and have a relevant signature on the absorption spectrum. Typically, the complex light-driven dynamics requires a theoretical modeling for shedding light on the time-dependent changes in the spectrum. Here we construct a semiconductor Bloch equation model for resolving the light-induced and core-electron dynamics simultaneously, which enables to easily disentangle the interband and intraband contributions. By using the Bloch model, we demonstrate a universal feature on attosecond x-ray transient absorption spectra that emerges from the light-induced coherent intraband dynamics. This feature is linked to previous studies of light-induced Fano resonances in atomic systems.

A reliable algorithm for fractional Bloch model arising in magnetic resonance imaging

Magnetic resonance imaging (MRI) is used in physics, chemistry, engineering and medicine to study complex materials. In this paper, numerical solution of fractional Bloch equations in MRI is obtained using fractional variation iteration method (FVIM) and fractional homotopy perturbation transform method (FHPTM). Sufficient conditions for the convergence of FVIM and its error estimate are established. The obtained results are compared with the existing as well as recently developed methods and with the exact solution. The obtained numerical results for different fractional values of time derivative are discussed with the help of figures and tables. Figures are drawn using the Maple package. Test examples are provided to illustrate the accuracy and competency of the proposed schemes.

Collisional dissipation of the laser-induced alignment of ethane gas: Energy corrected sudden quantum model.

We present the first quantum mechanical model of the collisional dissipation of the alignment of a gas of symmetric-top molecules (ethane) impulsively induced by a linearly polarized non-resonant laser field. The approach is based on use of the Bloch model and of the Markov and secular approximations in which the effects of collisions are taken into account through the state-to-state rates associated with exchanges among the various rotational states. These rates are constructed using the Energy Corrected Sudden (ECS) approximation with (a few) input parameters obtained independently from fits of the pressure-broadening coefficients of ethane absorption lines. Based on knowledge of the laser pulse characteristics and on these rates, the time-dependent equation driving the evolution of the density matrix during and after the laser pulse is solved and the time dependence of the so-called "alignment factor" is computed. Comparisons with measurements, free of any adjusted parameter, show that the proposed approach leads to good agreement with measurements. The analysis of the ECS state-to-state collisional rates demonstrates that, as in the case of linear molecules, collision-induced changes of the rotational angular momentum orientation are slower than those of its magnitude. This explains why the collisional decay of the permanent component of the alignment is significantly slower than that of the amplitudes of the transient revivals in both experimental and computed results. It is also shown that, since intermolecular forces within C2H6 colliding pairs weakly depend on rotations of the molecules around their C-C bond, the dissipation mechanism of the alignment in pure ethane is close to that involved in linear molecules.