Quantitative susceptibility mapping (QSM) uses gradient recalled echo MRI phase images and is a promising measure since it maps a physical tissue parameter.¹ QSM has been used to study iron levels, multiple sclerosis, traumatic brain injury, calcifications and contrast agent distribution.² Although various QSM pipelines have been proposed, there is still a lack of standardization for the generation of these parametric maps. Moreover, it is still unclear which factors influence the magnetic susceptibility at the voxel level. Frequency shift maps derived from phase images have been shown to be echo time dependent in white matter. A three compartment signal model (interstitial water, intra-axonal water and myelin water) was used to explain the non-linear trend in susceptibility.³ Although compartmentalisation of susceptibility has been used to explain the frequency shift trend in white matter, the trend in QSM response has not been studied in either gray or white matter. If a temporal trend in QSM can be shown across the brain, then it is plausible that methods exploring changes in cytoarchitecture and susceptibility compartments and chemical composition can be developed. Therefore, our aim is to study how QSM changes with echo time in several regions in the human brain, and whether these changes are specific to brain regions.

The local human ethics committee approved this study and written informed consent was given by five healthy participants (aged 30,31,32,34 and 41). 3D gradient recalled echo non-flow compensated scans were conducted on a 7T ultra-high field whole-body MRI research scanner (Siemens Healthcare, Erlangen, Germany) with a 32 channel dedicated head coil (Nova Medical, Wilmington, USA) using the following parameters: TE₁ = 2.04ms , echo spacing = 1.53ms, 30 echoes, TR = 51ms, flip angle = 15^o, voxel size = $$$1mm \times 1mm \times 1mm$$$ and matrix size = $$$210 \times 168 \times 144$$$. Fig 1 shows the QSM pipeline implemented in this study. Masks were derived based on magnitude data using the brain extraction tool provided in MIPAV(Medical Imaging Processing and Visualisation) for each channel.⁴ iHARPERELLA was used for phase processing and iLSQR for generating susceptibility maps (STI Suite package).⁵ The region of interests (ROIs), caudate, pallidum, putamen, thalamus, internal capsule, red nucleus, insula, corpus callosum, substantia nigra and fornix were segmented manually with the aid of a human brain atlas (shown in Fig 2).⁶ All scripts were implemented in MATLAB^®. A three compartment signal model was used to study susceptibility influences:

$$S\left(t\right)=A_{1}e^{-\frac{t}{T_{2,1}^*}-\iota\gamma{\chi_{1}{B_{0}t}}}+A_{2}e^{-\frac{t}{T_{2,2}^*}-\iota\gamma{\chi_{2}{B_{0}t}}}+A_{3}e^{-\frac{t}{T_{2,3}^*}-\iota\gamma{\chi_{3}{B_{0}t}}}.\it$$

In Fig 3, magnetic susceptibility has been plotted across 30 echo times for five participants for the ten brain regions defined in Fig 2. The thick solid line represents the mean values computed at each echo time from the five participant data, and dashed lines represent one standard deviation either side of the mean. The thin lines show the individual participant’s susceptibility curves. We found that each region elicits a different trend in the temporal susceptibility result. The results of fitting the three compartment model are provided in Tab 1. The adjusted R² signifies the quality of fit achieved in the fitting process, as shown in Fig 4. Out of the ten regions considered, only in the pallidum a good fit (R²=0.42) was not achieved, indicating the region is possibly more complex then explainable via a three compartment model. The ten brain regions are known to have different tissue microstructure and composition and the temporal susceptibility plots were found to be different. An adapted three component model and optimization to fit the experimental result was able to be used to parameterize image voxel susceptibility compartments. Echo time dependencies on frequency shift maps in myelinated white matter and presence oligodendrocytes and iron resulting in magnetic susceptibility deviation indicates that the potential reason for changing susceptibility could be due to different cytoarchitectures.^7,8 Similar neuronal bodies can be found in the caudate and putamen⁹ and we found similar susceptibility values in these regions (0.08ppm for the caudate and 0.07ppm for the putamen), shown in Table 1. Susceptibility values might also be influenced by the size, complexity and anisotropy of tissue structures. The flat response in the case of the thalamus could be due to its heterogeneity as it contains various nuclei which could cancel out the effects at the voxel level. Similarities in compartment susceptibilities across different brain regions, provided in Tab 1, may inform on tissue constituents.QSM is assumed to measure tissue susceptibility. Our work demonstrates that microstructural influences possibly influence magnetic susceptibility at the voxel level both in gray and white matter.