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Influence of model settings on myelin water fraction and frequency distribution for gradient-echo MRI at 7 Telsa
Kiran Thapaliya1, Viktor Vegh1, Steffen Bollmann1, and Markus Barth1

1The University of Queensland, Brisbane, Australia

### Synopsis

Quantitative assessment of model parameters (water fraction and frequency shift) estimated using a multi-compartment model can be useful to study tissue properties in white matter. In this work, we utilise multi-compartment models for multi-echo gradient echo data acquired at 7T. We investigate the variation of model parameters that could potentially be affected by differences in tissue microstructure in the corpus callosum. We further study the effect of different models (number of compartments and parameters) on the estimation of tissue parameters. We show that the tissue parameters vary across the sub-regions of the corpus callosum and are effected by different modelling choices.

### INTRODUCTION

Tissue microstructure has been shown to influence the measured gradient echo signal which can be explained by compartmentalising the voxel signal into distinct white matter (WM) signal components. WM compartments have been associated with myelin, axonal and extracellular spaces with specific $T_2^*$ relaxation times and frequency shifts.$1–5$ Existing studies have used different number of compartments and model parameters and observed differences in the estimated myelin water fraction and frequency shift in genu and splenium of the corpus callosum (CC). This could be due to experimental differences (number of echo times, echo spacing or field strength), model settings (number of compartments, model complexity), or use of different methods of optimisation. Here we investigate the influence of different model settings to examine the effect on tissue parameter estimates in the corpus callosum.

### METHODS

The study was approved by the university human ethics committee and written informed consent was obtained from ten healthy participants (aged 30-41). The data were acquired using a 3D GRE-MRI sequence on a 7T whole-body MRI research scanner (Siemens Healthcare, Erlangen, Germany) with a 32 channel head coil (Nova Medical, Wilmington, USA) using the following parameters: TE1=2.04ms with echo spacing of 1.53ms and 30 echoes, TR=51ms, flip-angle=20o, voxel-size=1mm$\times$1mm$\times$1mm and matrix size=210$\times$168$\times$144. Individual channel data were processed before images were combined.$6$ A brain mask for each participant was created using FSL BET.$7$ iHARPERELLA (http://people.duke.edu/~cl160, STI Suite$8$) was used to compute tissue phase for each echo. The CC was manually segmented into three and seven sub-regions, respectively, using a standardised template$9$ (Fig.1) to assess variation of tissue parameters across the CC and for a comparison with literature values. The three regions and whole CC were used to investigate the distribution of frequency shifts (Fig.2), whereas seven regions segmentation was used to estimate water fractions and frequency shifts (Fig.3). We also performed a voxel based analysis of CC (Fig.3). Signal fitting was performed using a three compartment (7 parameter) and two compartment (5 parameter) model::

$$S(t)=A_{1}e^{-\left(\frac{1}{T_{2,1}^*}+i2\pi\Delta f_{1}\right)t}+A_{2+3}e^{-\left(\frac{1}{T_{2,2}^*}+i2\pi\Delta f_{2}\right)t} (1)$$

$$S(t)=A_{1}e^{-\left(\frac{1}{T_{2,1}^*}+i2\pi\Delta f_{1}\right)t}+A_{2}e^{-\left(\frac{1}{T_{2,2}^*}+i2\pi\Delta f_{2}\right)t}+A_{3}e^{-\left(\frac{1}{T_{2,2}^*}+i2\pi\Delta f_{3}\right)t} (2)$$

where $A_{1}$, $A_{2}$ and $A_{3}$ are water fraction for the myelin, axonal, and extracellular compartments, or or combined axonal and extracellular compartments $(A_{2+3})$ respectively, and corresponding $T_{2,1}^*$, $T_{2,2}^*$ and $\Delta f_1$, $\Delta f_{2}$ and $\Delta f_{3}$ are the compartment relaxation times and frequency shifts. In Eqs. 1 and 2, the relaxation time of the myelin compartment was set to 7 ms4, and the relaxation time of the axonal and extracellular compartments were made the same$10$. Parameter fitting was performed in MATLAB (MathWorks, Natick, MA) using nonlinear curve fitting method (lsqnonlin). The model performance was assessed by computing the standard error rate.

### RESULTS

Fig.2 shows the cumulative frequency distribution across the three CC sub-regions and the whole CC in all participants. The frequency distribution for myelin, axonal and extracellular spaces derived from the three compartment model is similar across the three regions of CC, whereas the two compartment model showed variation of myelin frequency distribution between the three sub-regions of the CC (blue arrows in Fig.2). Both, two and three compartment models showed similar results for the whole CC.

The voxel based analysis and 7-ROI results are shown in Fig.3. We found that myelin water fraction and frequency shift estimates were very similar at the anteiror and posterior end of the CC for both models. The variation of the axonal frequency shift had a similar trend across the sub-regions with a stronger variation for the three compartment model. These results are also reflected in the CC maps using the voxel based analysis (Fig.3, right hand side). The error rate of the fit was less than 10% and 15% for both models. Significant differences between two models (p<0.0005) across the CC were found for myelin water fractions and axonal frequency shifts.

### DISCUSSION AND CONCLUSION

The distribution of frequencies estimated from the three and two compartment model is similar to the simulation result shown by Sati et al.$2$ displayed in Fig.3. They observed a relatively flat distribution of myelin frequency between -15 to 50 Hz, whereas our results show a myelin frequency distribution within the same range here, but with distinct peaks, which warrants the further investigation of more realistic models of WM fibers. The estimation of myelin water fraction was different from previous studies,$4,5$ which as we show could be partly due to differences in model settings. The distribution of myelin frequency shifts provides richer information about the tissue properties in comparison to the mean frequency shift value due to the impact of myelin sheet properties on MR frequency distributions. Our findings also show that the estimation of tissue parameters is affected by model settings and complexity.

### Acknowledgements

KT acknowledges a University of Queensland international (UQI) PhD scholarship. MB acknowledges funding from the Australian Research Council Future Fellowship grant FT140100865. The authors acknowledge the facilities and scientific and technical assistance of the National Imaging Facility, a National Collaborative Research Infrastructure Strategy (NCRIS) capability, at the Centre for Advanced Imaging, The University of Queensland. VV acknowledges support from the Australian National Health and Medical Research Council (NHMRC APP1104933)

### References

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2. Sati, P. et al. Micro-compartment specific T2⁎ relaxation in the brain. NeuroImage 77, 268–278 (2013).

3. Nam, Y., Lee, J., Hwang, D. & Kim, D.-H. Improved estimation of myelin water fraction using complex model fitting. NeuroImage 116, 214–221 (2015).

4. Thapaliya, K., Bollmann, S., Vegh, V. & barth, M. Signal Compartments Modelled from 7T Multi-Echo GE Data Showed Variation Across the Corpus Callosum. in Proc. Intl. Soc. Mag. Reson. Med. 25 (2017).

5. Alonso-Ortiz, E., Levesque, I. R. & Pike, G. B. Impact of magnetic susceptibility anisotropy at 3 T and 7 T on T2*-based myelin water fraction imaging. NeuroImage (2017). doi:10.1016/j.neuroimage.2017.09.040

6. Bollmann, S., Zimmer, F., O’Brien, F., Vegh, V. & Barth, M. When to perform channel combination in 7 Tesla quantitative susceptibility mapping? in Organization of the Human Brain Mapping (2015).

7. Smith, S. M. et al. Advances in functional and structural MR image analysis and implementation as FSL. NeuroImage 23, S208–S219 (2004).

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### Figures

Fig. 1 Illustration of the location of the definition of seven (shown on the left side) and three (shown on the right side) regions of interest across the corpus callosum which were used to study tissue characteristics via signal compartmentalisation.

Fig.2 shows the frequency distribution across three regions and the whole CC accumulated over all 10 participants. The first row shows the myelin, axonal, and extracellular frequency distribution across genu, mid-body, splenium and whole CC estimated from the three compartment model and simulation result from Sati et al.$2$ $\Delta f_1$, $\Delta f_{2}$ and $\Delta f_{3}$ are the myelin (blue line), axonal (red line), and extracellular (green line) frequency shifts in Hz. The second row shows the frequency distributions for the two compartment model (axonal and extracellular now as red line).

Fig.3: ROI based fitting results obtained for the seven regions of the corpus callosum using the proposed two (blue lines) and three (green lines) compartment models across ten subjects (error bars reflect SD over subjects). The maps of corresponding tissue parameters in a single subject is shown on the right side. MWF=myelin water fraction, $\Delta f_{ms}$, =myelin frequency shift, $\Delta f_{afs}$, =axonal frequency shift, $\Delta f_2compart$= frequency shift from two compartment model, $\Delta f_3compart$= frequency shift from three compartment model in Hz.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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