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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 …
Optimization of spin-lock times for T1ρ map** of human knee cartilage with bi- and stretched-exponential models
Two optimization criteria based on Cramér-Rao Bounds are compared between each other
and with non-optimized schedules for T1ρ map** using synthetic data, model phantoms …
and with non-optimized schedules for T1ρ map** using synthetic data, model phantoms …
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 …
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 …
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 …
Tissue‐Specific T2* Biomarkers in Patellar Tendinopathy by Subregional Quantification Using 3D Ultrashort Echo Time MRI
SJ Breda, DHJ Poot, D Papp… - Journal of Magnetic …, 2020 - Wiley Online Library
Background Quantitative MRI of patellar tendinopathy (PT) can be challenging due to spatial
variation of T2* relaxation times. Purpose 1) To compare T2* quantification using a standard …
variation of T2* relaxation times. Purpose 1) To compare T2* quantification using a standard …
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 …