DEcomposition and Component Analysis of Exponential Signals (DECAES)

Table of contents

• DEcomposition and Component Analysis of Exponential Signals (DECAES)
• • Table of contents
  • Introduction
  • Installation
  • Updating DECAES
  • Myelin water imaging
  • Acknowledgements
  • Citing this work
• Command Line Interface
• • Using the CLI
  • File types
  • Arguments
  • Outputs
  • Examples
• API Reference
• • $T_2$-distribution mapping
  • $T_2$-parts and the myelin water fraction
  • Main entrypoint function
  • NNLS analysis
  • Extended phase graph algorithm
• Internals
• • CLI submodule
  • NNLS submodule

Introduction

DECAES decomposes multiexponential signals from multi-spin echo magnetic resonance imaging (MRI) into exponential components by solving the regularized nonnegative least-squares (NNLS) problem

\[x_{\mu} = \underset{x \ge 0}{\operatorname{argmin}}\; \lVert Ax - b\rVert_2^2 + \mu^2 \lVert x\rVert_2^2,\]

where $b$ is the signal magnitude, $A$ contains exponential decay bases constructed using the extended phase graph (EPG) algorithm with stimulated echo correction, and $\mu$ is the regularization parameter. Each component $x_{\mu,j}$ is the nonnegative amplitude associated with decay time $T_{2,j}$, so $x_\mu$ is called the $T_2$ distribution.

Installation

Install DECAES using Julia v1.9 or later:

julia --project=@decaes -e 'import Pkg; Pkg.add("DECAES"); Pkg.build("DECAES")'

This installs DECAES in the named project @decaes and builds the command-line launcher ~/.julia/bin/decaes.

Updating DECAES

Update DECAES with:

julia --project=@decaes -e 'import Pkg; Pkg.update("DECAES"); Pkg.build("DECAES")'

Myelin water imaging

Myelin water imaging (MWI) uses $T_2$ distributions from multi-spin echo MRI to distinguish signal arising from myelin water and from intra- and extracellular water. The myelin water fraction (MWF) is the fraction of water associated with the short-$T_2$ myelin-water component. DECAES provides methods for computing the MWF.

MWI was pioneered at the University of British Columbia by Alex MacKay and Ken Whittal.

Basics of myelin water imaging:

• https://doi.org/10.1002/mrm.1910310614
• https://doi.org/10.1016/0022-2364(89)90011-5
• https://doi.org/10.1016/j.neuroimage.2012.06.064
• https://doi.org/10.1002/mrm.23157

Validation of myelin water imaging:

• https://doi.org/10.1016/j.neuroimage.2007.12.008
• https://doi.org/10.1016/j.neuroimage.2017.03.065
• https://doi.org/10.1016/j.neuroimage.2019.05.042

Some applications of myelin water imaging:

• https://doi.org/10.1177/1352458517723717
• https://doi.org/10.1038/s41598-018-33112-8
• https://doi.org/10.1371/journal.pone.0150215

Acknowledgements

• Porting to Julia was done by Jonathan Doucette (email: jdoucette@physics.ubc.ca) in November 2019. This work was funded by NSERC (016-05371) and CIHR (RN382474-418628) under PI Alexander Rauscher at the University of British Columbia
• Christian Kames (email: ckames@physics.ubc.ca) contributed to optimizing the Julia port for both speed and memory efficiency, as well as writing the PAR/XML/REC file reader used internally
• Original MATLAB code was written by Thomas Prasloski (email: tprasloski@gmail.com). Modifications to the MATLAB code were made by Vanessa Wiggermann to enable processing on various MATLAB versions in February 2019. The Julia port is based on this modified version

Citing this work

If you use DECAES in your research, please cite the following:

@article{DECAES.jl-2020,
  title = {{{DECAES}} - {{DEcomposition}} and {{Component Analysis}} of {{Exponential Signals}}},
  author = {Doucette, Jonathan and Kames, Christian and Rauscher, Alexander},
  year = {2020},
  month = may,
  issn = {1876-4436},
  doi = {10.1016/j.zemedi.2020.04.001},
  journal = {Zeitschrift Fur Medizinische Physik},
  keywords = {Brain,Luminal Water Imaging,MRI,Myelin Water Imaging,Prostate},
  language = {eng},
  pmid = {32451148}
}