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

作者：

Highlights：

• The utility of the distributed-order time fractional Bloch model is considered.

• Three models of continuous distribution weight functions are considered.

• An effective implicit numerical method implemented on a graded mesh was proposed.

• Semi-analytical solutions are derived to assess the computational model accuracy.

• The models are able to characterize anomalous relaxation processes in MRI data.

摘要

•The utility of the distributed-order time fractional Bloch model is considered.•Three models of continuous distribution weight functions are considered.•An effective implicit numerical method implemented on a graded mesh was proposed.•Semi-analytical solutions are derived to assess the computational model accuracy.•The models are able to characterize anomalous relaxation processes in MRI data.

论文关键词：Distributed-order time fractional Bloch equations,Anomalous relaxation,Truncated normal distribution,Beta distribution,Graded mesh,Parameter estimation

论文评审过程：Received 24 March 2021, Revised 28 March 2022, Accepted 15 April 2022, Available online 25 April 2022, Version of Record 25 April 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127188