Quantitive Susceptibility Mapping

Overview

The goal of QSM is to recover information about the the magnetic properties of brain tissue (its susceptibility value). This manifests as magnetic field changes generated (primarily) by iron in tissue and this can be detected using certain MR imaging sequences (gradient-echo). The degree of field change is directly proportional to the quantity of substance in the tissues. This is currently useful for certain structures - particularly deep grey matter as the field here seems to be dominated by iron (see Langkammer C et al. NeuroImage 2012 and his infamous Figure 3) and so is likely proportional specifically to iron concentration.

As you can imagine, getting at this subtle, local field information is tricky and easily contaminated by other factors (global imperfections in our magnet, etc.). The maths behind recovering the information is conceptually simple but is in fact rather difficult to implement in practice. For example there are lots of points in creating the map where the QSM algorithm will be trying to divide by zero. Thus recovering the QSM value (going from ‘field to source’) in susceptibility research is often referred to as an ‘ill-posed problem’.

The following figure from Ferdinand Schweser illustrates the QSM problem:

_images/qsm_summary.png

Note

The main issue with QSM is that there is currently no agreed protocol on the MRI side for acquiring QSM images and a multitude of software packages to do the QSM processing. I’ve only included a brief survey of the available methods below. For a more exhaustive description please do an up-to-date literature search.

Steps and theory

  1. Data Acquisition

We acquire the data using a T2* sequence in order to collect field information (this does not correct for the local field inhomogeneities — unlike a T2/spin-echo sequence). For MS Gait we are using a 9-echo bipolar multi-echo sequence as this gives us the opportunity to average QSM maps from a number of echoes (as opposed to the minimum of one echo) to a obtain a ‘higher-quality’ mean map.

We use the phase images from the MRI scanner to eventually create the QSM map. MRI data is complex and has real and imaginary components. These two components are needed for the Fourier transform to work properly. On an Argand diagram, we can express these components geometrically. This allows us to calculate the actual magnitude image. But we can also see the phase difference (ϕ) between the real and imaginary components. (Until a few years ago, this phase information was usually discarded as it was felt to contain little useful information).

  1. Multi coil combining & phase offset correction

Given that most current MRI scanners have multiple receiver coils, the data from each coil must be combined to form a single image. This is commonly done with sum of squares. Phase offsets can be calculated using a number of approaches. We have recently proposed a unique solution to this problem (POEM, under revision at MRM) that also allows for correct of odd and even echo offsets for bipolar gradients (another ongoing issue).

  1. Phase unwrapping

The combined phase images contains data that is wrapped between -pi and pi. Large phase changes due to field inhomogeities outside the brain cause the phase to wrap repeatedly around the -pi to pi interval. This must be unwrapped. Several techniques exist to solve this problem including Laplacian methods, PRELUDE, path-based methods and others. We use best path, a path based method that is fast and relatively reliable. Best path identifies the largest homogeneous region, then traces a path through the biggest wrap and so on until it reaches a solution. Best path can imperfectly unwrap around the edges of the image or in regions of strong susceptibility so we are currently working on a method for post-processing best-path to correct this. Once the phase is unwrapped, phase images from multiple echos are fit with linear regression to calculate the total field shift for each voxel.

  1. Background phase removal

Total field shift includes local susceptibility sources inside the brain, and phase changes due to large susceptibility sources (e.g. air) outside the brain. We are only interested in the local field shift so a background phase removal method is used to isolate this from the total field shift. Background phase removal is generally performed using a form of 3D image high pass filtering because the background phase tends to be slowly varying and large.

  1. Calculate the QSM value from the local field shift

To calculate the QSM, commonly referred to as χ (chi), it is necessary to deconvolve the local field shift image with a dipole kernel. TBC

Thanks to Jon Cleary for writing much of this great summary.