Fractional calculus models of magnetic resonance phenomena: relaxation and diffusion

R Magin, MG Hall, MM Karaman… - Critical Reviews™ in …, 2020 - dl.begellhouse.com
Applications of fractional calculus in magnetic resonance imaging (MRI) have increased
over the last twenty years. From the mathematical, computational, and biophysical …

Chaos in the fractional order nonlinear Bloch equation with delay

D Baleanu, RL Magin, S Bhalekar… - … in Nonlinear Science …, 2015 - Elsevier
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 …

Second-order BDF time approximation for Riesz space-fractional diffusion equations

H Liao, P Lyu, S Vong - International Journal of Computer …, 2018 - Taylor & Francis
Second-order backward difference formula (BDF2) is considered for time approximation of
Riesz space-fractional diffusion equations. The Riesz space derivative is approximated by …

Longitudinal study using voxel‐based relaxometry: Association between cartilage T and T2 and patient reported outcome changes in hip osteoarthritis

V Pedoia, MC Gallo, RB Souza… - Journal of Magnetic …, 2017 - Wiley Online Library
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 …

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

Q Yu, I Turner, F Liu, V Vegh - Applied Mathematics and Computation, 2022 - Elsevier
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 T2 relaxation in normal and degraded cartilage

DA Reiter, RL Magin, W Li, JJ Trujillo… - Magnetic resonance …, 2016 - Wiley Online Library
Purpose To compare the ordinary monoexponential model with three anomalous relaxation
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 …

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 …