Article
Mathematics, Applied
Kamel Hamdache, Djamila Hamroun
Summary: This work aims to investigate the diffusion of various models of the Kinetic-Bloch system through asymptotic analysis. The limit of the kinetic equation under classical diffusion scaling reveals that the magnetization field aligns parallel to the magnetic field. Furthermore, by applying a second scaling of the kinetic equation, it is demonstrated that the dynamics of magnetization is governed by the Bloch-Torrey diffusion equation.
MEDITERRANEAN JOURNAL OF MATHEMATICS
(2023)
Article
Biophysics
Syver Doving Agdestein, Try Nguyen Tran, Jing-Rebecca Li
Summary: This study extends a previous simulation framework to include geometries with permeable cell membranes, describing the new computational techniques that allow this generalization and analyzing the effects of permeability coefficient magnitude on the eigendecomposition of diffusion and Bloch-Torrey operators. This work represents another advancement in incorporating advanced mathematical tools and numerical methods into the simulation and modeling of diffusion MRI.
NMR IN BIOMEDICINE
(2022)
Article
Mathematics, Applied
Marwa Kchaou, Jing-Rebecca Li
Summary: Based on a reference partial differential equation model, this paper uses periodic homogenization theory to establish macroscopic models. A higher order asymptotic model is formulated to handle higher values of permeability, and a system of ordinary differential equations is solved to model the diffusion MRI signal. Numerical results demonstrate the improved accuracy of the new model in the regime of higher permeability.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2023)
Article
Engineering, Biomedical
Zheyi Yang, Chengran Fang, Jing-Rebecca Li
Summary: In this paper, a new formulation of the permeable diffusion MRI signal representation is proposed, which is based on the Laplace eigenfunctions of the medium. The computational efficiency of the forward solution for multiple permeability values is improved.
PHYSICS IN MEDICINE AND BIOLOGY
(2023)
Article
Physics, Multidisciplinary
Nicolas Moutal, Denis S. Grebenkov
Summary: This article investigates the peculiar feature of non-Hermitian operators, namely the existence of spectral branch points, and provides a pedagogic introduction to this phenomenon with the example of 2x2 - backward difference 2-igx.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Computer Science, Artificial Intelligence
Chengran Fang, Zheyi Yang, Demian Wassermann, Jing-Rebecca Li
Summary: A framework is proposed to train supervised learning models on synthetic data for estimating brain microstructure parameters using diffusion magnetic resonance imaging (dMRI). The trained models perform well on synthetic test sets and give promising results on real data.
MEDICAL IMAGE ANALYSIS
(2023)
Article
Optics
Peng He, Yu-Guo Liu, Jian-Te Wang, Shi-Liang Zhu
Summary: The study explores the damping dynamics of single-particle correlation in an open system under periodic and aperiodic order, revealing the existence of non-Hermitian skin effect and chiral damping. The system displays sensitivity to boundary conditions due to the non-Hermitian skin effect, and undergoes phase transitions with hopping amplitude modulation. The presence of phase transitions is demonstrated through spectral topology analysis, and the coexistence of non-Hermitian skin effect and Anderson localization is identified in the incommensurate case.
Article
Mathematics, Applied
Mengchen Zhang, Fawang Liu, Ian W. Turner, Vo V. Anh
Summary: This paper investigates the suitability of a fractional Laplacian in constructing a three-dimensional multi-term time-space fractional Bloch-Torrey equation. The authors propose a numerical method using matrix function approximations to discretize the equation and show its feasibility and effectiveness through numerical examples.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
K. Sayevand, N. Ghanbari, I Masti
Summary: This study presents a numerical-based solution for the time-space fractional Bloch-Torrey equation using the Crank-Nicolson weighted shifted Grunwald difference method, and investigates the stability and solvability of this method. The results show that the method is of order O(tau(2-alpha), h(2)), where 0 < alpha < 1, and it is more efficient in terms of accuracy and CPU time compared to existing schemes in open literature.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Libo Feng, Fawang Liu, Vo V. Anh
Summary: This paper discusses a two-dimensional tempered time-space fractional diffusion equation with a reaction term on convex domains. The analytical solution to a one-dimensional tempered time-space diffusion equation is obtained using the Fox H function, while for the two-dimensional case, an explicit expression for its analytical solution is intractable. Numerical methods are thus employed, including the modification of the L1 formula on a graded mesh and the development of a fast evaluation for the tempered time-fractional operator. The Galerkin finite element method on an unstructured mesh is utilized for solving the problem, and two numerical examples in different convex domains are investigated to demonstrate the effectiveness of the numerical method. The impact of the tempered parameter on the decay of magnetization is also observed in the application of the tempered fractional Bloch-Torrey equation in a human brain-like domain.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Mengchen Zhang, Fawang Liu, Ian W. Turner, Vo V. Anh, Libo Feng
Summary: In this study, a new generalised two-dimensional time and space variable-order fractional Bloch-Torrey equation is developed to simulate diffusion phenomena in biological tissues. The accuracy of the numerical method is improved and verified in various biological micro-environments.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Weiping Bu, Yanmin Zhao, Chen Shen
Summary: This paper proposes a numerical approach combining finite difference method and finite element method to solve the two-dimensional time-space fractional Bloch-Torrey equation. The numerical scheme is based on coupled equations and utilizes an efficient sum-of-exponentials approximation. Stability, convergence, and error estimation are discussed, and numerical tests are provided to demonstrate the effectiveness of the proposed method.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Clinical Neurology
Ashishi Puri, Snehlata Shakya, Sanjeev Kumar
Summary: This paper presents an algorithm for reconstructing the brain's white matter fibers using diffusion MRI data. A fractional order mixture of central Wishart (FMoCW) model is proposed, which efficiently distinguishes multiple fibers even with small angles of separation. The proposed model outperforms other existing models in terms of angular error.
PSYCHIATRY RESEARCH-NEUROIMAGING
(2023)
Article
Optics
Helene Wetter, Zlata Fedorova, Stefan Linden
Summary: Using evanescently coupled waveguides, we investigated the propagation of surface plasmon polaritons and observed plasmonic analogs of Bloch oscillations and the Wannier-Stark ladder.
Article
Optics
Stefano Longhi
Summary: In non-Hermitian quasicrystals, the mobility edges (ME) that separate localized and extended states in the complex energy plane are of topological nature. The origin of non-Hermiticity determines the transport features, with different winding numbers corresponding to either ballistic transport or pseudo-dynamical localization.
