Abstract

PURPOSE – Abnormal accumulation of iron in the brain is known to be associated with several neurodegenerative diseases such as multiple sclerosis or Parkinson’s disease. Hence, a major research focus currently lies on developing and applying non-invasive techniques to assess the iron concentration in the brain. Quantitative susceptibility mapping (QSM) allows assessing the bulk tissue magnetic susceptibility which is, by its very nature, linear to the average iron concentration in the tissue. The R2 relaxation rate has also recently been shown to be linear to the iron concentration, which is remarkable, because in the presence of small inclusions R2 cannot be described by the static dephasing regime and, consequently, depends in a non-linear way on the compartmentalization of the iron. R2 may, in principle, change even if the total amount of iron in the tissue remains constant but the compartmentalization of the iron changes, e.g., due to the breakdown of iron-containing cells. In this contribution we show how a combination of R2 mapping and QSM can be used to infer on the compartmentalization of brain iron in vivo. THEORY – The transverse relaxation rate R2 due to susceptibility inclusions (index “inc”), such as iron, depends on the contribution of the inclusions to the voxel magnetic susceptibility χ, their effective size (radius Rinc), and their susceptibility difference Δχinc relative to the parenchyma as well as of the diffusion coefficient D in the vicinity of the inclusions: (R2) = χ -1 ⋅ [405/16⋅D (RincγB0) (Δχinc) + 9⋅3/(2πγB0)] (1). In this context susceptibility inclusions are the smallest particles with a susceptibility difference seen by diffusing spins. These could, e.g., be iron-laden cells or freely dissolved aggregated iron clusters. The ratio χ/R2 ≡κ is independent of the total iron concentration (χ) in the voxel. Using D=2.8⋅10 m/s yields at 3T κ = 1.10⋅10 ppm⋅s⋅m ⋅ Rinc ⋅ Δχinc + 3.09⋅10 ppm⋅s (2). The right-most term in this Equation represents R2 in the static dephasing regime. Expressing Δχinc as a function of the number of iron atoms Ninc in the inclusion, Δχinc = 2.96⋅10 ppm⋅m ⋅ Ninc/Rinc, shows that κ (in Eq. (2)) is a function of the ratio of Rinc and Ninc: Rinc/Ninc = (κ 3.09⋅10 ppm⋅s) / 3.72⋅10 ppm⋅s⋅m (3). κ may be determined, for example, by linear regression of χ and R2 in regions with different iron content, e.g. in the basal ganglia. METHODS – Data Acquisition and Processing: Double-echo gradient echo data were acquired from four healthy volunteers (male; 26-28 year old) on a 3T whole-body MRI scanner (Tim Trio, Siemens Medical Solutions, Erlangen, Germany) with the ToF-SWI-sequence. R2 maps were calculated from the magnitude images using the power method with logarithmic calculus and compensation of macroscopic field gradient contributions. Phase aliasing was resolved and susceptibility maps were calculated from the second echo with the HEIDI algorithm. Evaluation: ROIs were drawn manually in the basal ganglia nuclei using MRIcro (Version 1.39, 2005. Chris Rorden, Atlanta, GA). Rigorous least squares regression of R2 and susceptibility voxel values was performed for each volunteer inside the ROIs. RESULTS – Figure 1 shows maps of R2 and magnetic susceptibility of an exemplary volunteer. Figure 2 presents the correlation of the corresponding voxel values in the basal ganglia. The average slope obtained by the linear regression in all volunteers was κ = 0.0054 ppm⋅s (range: 0.0047 to 0.0064 ppm⋅s; R>0.6, p<10). Figure 3 illustrates potential configurations of iron storage, Rinc and Ninc, as a function of κ according to Eq. 3. The vertical black line in Fig. 3 marks the measured κ. DISCUSSION – It has been shown that the ratio κ of susceptibility and R2 allows assessing the compartmentalization of the iron (Eq. 3 and Fig. 3). The volunteer results lead to three important implications: First, κ > 3.09⋅10 ppm⋅s (cf. Eq. 2) shows that R2 due to brain iron cannot be described in the static dephasing regime, meaning that the compartmentalization of iron has a substantial effect on R2 and must not be neglected. Second, using Ninc=1000 for H-rich ferritin (dominant in the brain) yields Rinc=0.62 pm which is considerably less than the size of a single iron atom (R≈125 pm). This suggests a substantially higher number of iron atoms per inclusion, which is consistent with the histologic finding that ferritin agglomerates in oligodendrocytes, with a radius of approximately 2.5 μm. Knowing that iron occurs predominantly in oligodendrocytes (horizontal black line in Fig. 3) points to an average number of 4⋅10 iron atoms per oligodendrocyte, or Δχinc=7.6 ppm. In the substantia nigra, for example, χFe=0.2 ppm, leading to a relative volume fraction of oligodendrocytes of approximately 2.6%, which is in good agreement with histology. Third and most interesting, the linear relation between R2 and susceptibility (Fig. 2) indicates that the iron loading of oligodendrocytes (reflected by κ through Eq. 3) is similar throughout the deep brain nuclei meaning that susceptibility and R2 differences are due to different volume density of oligodendrocytes, rather than due to different loading factors of ferritin or number of ferritin molecules. This conclusion relies, of course, on the assumption that the average size of the oligodendrocytes does not vary considerably throughout the different nuclei, which seems, however, reasonable. It may be hypothesized that under pathologic conditions the iron load rather than the volume density of the oligodendrocytes changes, resulting in a decrease of κ according to Eq. (3), and, consequently, an increase of the number of iron atoms per cell (Fig. 3), changing the relation between susceptibility and R2. Thus, a combined analysis of R2 and bulk magnetic susceptibility may give insights into pathologic iron deposition beyond the local changes of the iron concentration, e.g. into the breakdown of oligodendrocytes, and will be investigated in future studies. Combination of the proposed method with techniques for determining the incusion size, e.g. combination of T2 and T2, may improve the estimate of the oligodendrocyte iron load. CONCLUSION – Combining R2 mapping and QSM allows investigating the ratio of the size and the iron load of iron-containing cells in vivo. The biophysical insights revealed by this approach bear the potential to be more specific to pathologic conditions than measurements of R2 and susceptibility alone. ACKNOWLEDGEMENT – We are grateful to Christian Ziener (University of Heidelberg, Germany) and Thomas Kampf (University of Würzburg, Germany) for valuable discussions on the relaxation properties of susceptibility inclusions.