Fractional calculus models of magnetic resonance phenomena: relaxation and diffusion
Applications of fractional calculus in magnetic resonance imaging (MRI) have increased
over the last twenty years. From the mathematical, computational, and biophysical …
over the last twenty years. From the mathematical, computational, and biophysical …
Chaos in the fractional order nonlinear Bloch equation with delay
The Bloch equation describes the dynamics of nuclear magnetization in the presence of
static and time-varying magnetic fields. In this paper we extend a nonlinear model of the …
static and time-varying magnetic fields. In this paper we extend a nonlinear model of the …
Second-order BDF time approximation for Riesz space-fractional diffusion equations
Second-order backward difference formula (BDF2) is considered for time approximation of
Riesz space-fractional diffusion equations. The Riesz space derivative is approximated by …
Riesz space-fractional diffusion equations. The Riesz space derivative is approximated by …
Elucidating the 1H NMR Relaxation Mechanism in Polydisperse Polymers and Bitumen Using Measurements, MD Simulations, and Models
The mechanism behind the 1H nuclear magnetic resonance (NMR) frequency dependence
of T 1 and the viscosity dependence of T 2 for polydisperse polymers and bitumen remains …
of T 1 and the viscosity dependence of T 2 for polydisperse polymers and bitumen remains …
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 …
the classical mono-exponential relaxation. This deviation is referred to in the literature as …
Longitudinal study using voxel‐based relaxometry: Association between cartilage T1ρ and T2 and patient reported outcome changes in hip osteoarthritis
Purpose To study the local distribution of hip cartilage T1ρ and T2 relaxation times and their
association with changes in patient reported outcome measures (PROMs) using a fully …
association with changes in patient reported outcome measures (PROMs) using a fully …
Fractal Bloch model to characterize stretched magnetization relaxation in magnetic resonance imaging
Y Liang, Y Yu - Communications in Nonlinear Science and Numerical …, 2023 - Elsevier
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 …
in magnetic resonance imaging (MRI). The fractal Bloch model extends the relaxation terms …
Chaos in a nonlinear Bloch system with Atangana–Baleanu fractional derivatives
JF Gómez‐Aguilar - Numerical Methods for Partial Differential …, 2018 - Wiley Online Library
In this article, a nonlinear model of the Bloch equation to include both fractional derivatives
with variable‐order, constant‐order, and time delays was considered. The fractional …
with variable‐order, constant‐order, and time delays was considered. The fractional …
Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D
Abstract Recently, the fractional Bloch-Torrey model has been used to study anomalous
diffusion in the human brain. In this paper, we consider three types of space and time …
diffusion in the human brain. In this paper, we consider three types of space and time …
Anomalous T2 relaxation in normal and degraded cartilage
Purpose To compare the ordinary monoexponential model with three anomalous relaxation
models—the stretched Mittag‐Leffler, stretched exponential, and biexponential functions …
models—the stretched Mittag‐Leffler, stretched exponential, and biexponential functions …