Synopsis

In this work, we explored an alternative approach of using nominal $R_2^{\:'}$ instead of measured $R_2^{\:'}$ in separating the two susceptibility sources. The linear relationship between $R_2^{*}$ and $R_2^{\:'}$ was investigated and used to obtain the nominal $R_2^{\:'}$ values. The positive and negative magnetic susceptibility source maps using nominal $R_2^{\:'}$ showed similar susceptibility distribution to the map using measured $R_2^{\:'}$.

Introduction

Recently, a new QSM algorithm that separates positive and negative susceptibility sources was proposed [1]. The method requires the estimation of $R_{2}^{\:'}$ which is defined as $R_{2}^{*}-R_{2}$ and, therefore, needs $R_{2}$ measurement. However, acquiring $R_{2}$ requires long scan time (10 min) and processing time (up to several hours) [2] and is not commonly performed in neuroimaging. In this work, we explored an alternative approach of using nominal $R_{2}^{\:'}$ instead of measured $R_{2}^{\:'}$ (= $R_{2,measured}^{\:'}$) in susceptibility source separation. The method was applied to healthy volunteers and multiple sclerosis (MS) patients and the resulting susceptibility maps were compared with those from $R_{2,measured}^{\:'}$.

Methods

[Estimating Nominal $R_{2}^{\:'}$]

It has been shown that both $R_{2}^{\:'}$ and $R_{2}^{*}$ can be modeled as a linear equation to tissue susceptibility concentration [3-5]. Therefore, we can infer that the relationship between $R_{2}^{\:'}$ and $R_{2}^{*}$ is also linear. It can be written as follows: $$R_{2}^{\:'} = a\cdot{R_{2}}^{*}+b\:\:\:\:\:\:Eq. [1]$$ Once the two coefficients, $a$ and $b$, are known, we can use $R_{2}^{*}$ to estimate a nominal value of $R_{2}^{\:'}$. To obtain the coefficients, two different approaches are tested. First, the measurements in a literature [3] lead to $a=0.78$ and $b=-6.07$. The estimated $R_{2}^{\:'}$ using these values is referred to as $R_{2,nominal,lit.}^{\:'}$ hereafter. The second approach is to acquire $R_{2}^{*}$ and $R_{2,measured}^{\:'}$ from in-vivo data and then generate the coefficients using linear regression. This $R_{2}^{\:'}$ is referred to as $R_{2,nominal,fit}^{\:'}$.

[Experiments and data processing]

Four healthy volunteers and three MS patients were scanned at 3T. For $R_{2}^{*}$, gradient-echo was acquired (healthy volunteers: resolution=1×1×2mm³, TR=53ms, and TE=5.1:5.0:30.0ms; MS patients: resolution=0.5×0.5×2mm³, TR=53ms, and TE=5.8:6.2:36.7ms). To estimate $R_{2,measured}^{\:'}$, $R_{2}$ was acquired using multi-echo spin-echo (healthy volunteers: resolution=1×1×2mm³, TR=2400ms, and TE=10:10:100ms; MS patients: resolution=0.5×0.5×2mm³, TR=1800ms, and TE=10:10:90ms). An $R_{2}^{*}$ map was generated by mono-exponential fitting to the multi-echo data. An $R_{2}$ map was generated after $EPG_{SLR}$ correction [2]. $R_{2}^{\:'}$ was calculated by subtracting $R_{2}$ from $R_{2}^{*}$. The positive and negative susceptibility maps were acquired using [1].

To estimate the coefficients of $R_{2,nominal,fit}^{\:'}$, a linear regression between $R_{2}^{*}$ and $R_{2,measured}^{\:'}$ was performed for voxels in five regions (SN, RN, CN, GP and PU) in healthy volunteers. No white matter region was included as $R_{2}^{*}$ has been shown to depend on not only susceptibility concentration but also fiber orientation [6, 7]. Outliers were removed using Cook’s distance [8]. The positive and negative susceptibility source maps from $R_{2,measured}^{\:'}$, $R_{2,nominal,fit}^{\:'}$, and $R_{2,nominal,lit.}^{\:'}$ were generated and compared. Thalamus, which includes iron-rich but myelin-lacking nuclei (pulvinar and nucleus medialis), and optic-radiation, which has myelin-rich but iron lacking region, were inspected [9-11]. The results were also compared in MS lesions.

Results

When relationship between $R_{2}^{*}$ and $R_{2}^{\:'}$ was explored, it showed a good linear relation (Fig. 1), agreeing with previous studies [3-5]. The slopes and offsets in [Eq. 1] of four healthy volunteers have similar values with small standard deviation ($slope=0.675\pm0.021$ and $offset=-8.21\pm0.499$). Hence, we used $R_{2,nominal,fit}^{\:'}=0.675\cdot{R_{2}}^{*}-8.21$ hereafter. From the literature [3], we found $R_{2,nominal,lit.}^{\:'}=0.78\cdot{R_{2}}^{*}-6.07$. The positive and negative susceptibility source maps of a healthy volunteer are shown in Fig. 2. Overall, the maps show similar contrast distribution. However, the positive susceptiblity map using $R_{2,nominal,lit.}^{\:'}$ was slightly overestimated (Fig. 2a and c right column). When thalamus was zoomed in, pulvinar and nucleus medialis are delineated in the negative susceptibility maps using $R_{2,measured}^{\:'}$ and $R_{2,nominal,fit}^{\:'}$ images (Fig. 2a and b left column and middle column).

In MS patient results, all the positive maps show two ring-shaped lesions (Fig. 3), indicating iron accumulation at the rim of the lesions [12]. One of them shows potentially a feeding vein inside the lesion (Fig. 3; red box), which was still detectable but less apparent in the nominal $R_{2}^{\:'}$ corrected images. The negative map using $R_{2,measured}^{\:'}$ shows a demyelinated lesion (Fig. 3d and e; green box), and a potentially partially remyelinated lesion (Fig. 3d and e; red box). Similar appearances are observed in the negative susceptibility maps using $R_{2,nominal,fit}^{\:'}$, and $R_{2,nominal,lit.}^{\:'}$.

Discussion and Conclusion

Acknowledgements

References

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