# Analyzing PFG anisotropic anomalous diffusions by instantaneous signal attenuation method

**Authors:** Guoxing Lin  
**arXiv:** [1701.00257](https://arxiv.org/abs/1701.00257)  
**Date:** 2017-01-01  
**Summary page:** https://www.summarizepaper.com/en/paper/1701.00257v2/

## Key points

- Pulsed Field Gradient (PFG) techniques extensively studied in anomalous diffusion field
- Anomalous diffusion more complex than normal diffusion when analyzed with PFG methods
- Limited study on anisotropic anomalous diffusion compared to isotropic anomalous diffusion
- Lack of general expression for PFG signal attenuation considering finite gradient pulse effect and accommodating all types of anisotropic fractional diffusions
- Guoxing Lin's paper introduces Instantaneous Signal Attenuation (ISA) method for deriving PFG signal attenuation expressions for free and restricted anisotropic anomalous diffusion
- Two models used: fractal derivative model and fractional derivative model
- Results consistent with existing results for PFG anisotropic normal diffusion and isotropic anomalous diffusion obtained through different methods
- Study extended to anisotropic space-fractional diffusion, aligning with results from modified Bloch equation method
- Traditional methods used to derive PFG signal attenuation expressions for free and restricted anisotropic curvilinear diffusions, agreeing with results based on fractional derivative model for PFG anisotropic fractional diffusions
- Discussion on powder pattern of PFG anisotropic diffusion providing valuable insights into understanding of processes
- Research offers new formalisms and advancements in analyzing PFG anisotropic anomalous diffusions in NMR and MRI applications

## Summary

In the field of anomalous diffusion, Pulsed Field Gradient (PFG) techniques have been extensively studied in various systems. Anomalous diffusion is known to be more complex than normal diffusion when analyzed using PFG methods. While there have been numerous theoretical and experimental investigations into PFG isotropic anomalous diffusion, the study of anisotropic anomalous diffusion has been relatively limited. One of the challenges in this area is the lack of a general expression for PFG signal attenuation that considers the finite gradient pulse effect and can accommodate all three types of anisotropic fractional diffusions: general fractional diffusion, time fractional diffusion, and space-fractional diffusion. This paper by Guoxing Lin presents a novel approach known as the Instantaneous Signal Attenuation (ISA) method to derive PFG signal attenuation expressions for both free and restricted anisotropic anomalous diffusion. Two models were utilized: the fractal derivative model and the fractional derivative model. The obtained expressions for anisotropic anomalous diffusion were shown to be consistent with existing results for PFG anisotropic normal diffusion as well as isotropic anomalous diffusion obtained through different methods such as effective phase shift diffusion equation and instantaneous signal attenuation. Furthermore, the study also extended to anisotropic space-fractional diffusion, where the derived results aligned with those obtained using the modified Bloch equation method. Additionally, traditional methods were used to derive PFG signal attenuation expressions for free and restricted anisotropic curvilinear diffusions, which were found to agree with results based on the fractional derivative model for PFG anisotropic fractional diffusions. The paper also delved into discussing the powder pattern of PFG anisotropic diffusion, providing valuable insights that contribute to a deeper understanding of PFG anomalous diffusion processes. Overall, this research offers new formalisms and advancements in analyzing PFG anisotropic anomalous diffusions in NMR and MRI applications, showcasing significant progress in this specialized area of study.