Synopsis

In this study, we propose a new scaling approach that translates myelin water fraction into myelin volume fraction using the geometric property of myelin. The method is validated by a histo-imaging dataset. A computer simulation is performed to demonstrate the robustness of the method.

Introduction

Methods

[Scaling process] In MWI, the signal amplitude (A) of each compartment (myelin (my), axon (ax), and extracellular space (ex)) is proportional to its volume (V) and MR-visible volume ratio ($κ$=MR-visible volume/total volume of the compartment): $$A∝κ·V.\qquad(1)$$ Then, MVF is expressed as follows: $$MVF=\frac{V_{my}}{V_{my}+V_{ax}+V_{ex}}=\frac{A_{my}/κ_{my}}{A_{my}/κ_{my}+A_{ax}/κ_{ax}+A_{ex}/κ_{ex}}.\qquad(2)$$ To estimate $κ_{my}$, we calculated MR-visible myelin volume and the total myelin volume using the geometry of myelin. The total volume of myelin consists of MWV and MLV, of which only MWV is considered to be MR-visible volume. Considering the length ($l$) of the myelinated axon with the number of lamellae (n) (Fig. 1a), MWV and MLV volume are calculated as the sum of the alternating volumes of the concentric cylinders: $$MWV=∑_{i=1}^{2n}π [\{(w_{lip}+w_{water})×i+r_{ax}\}^2-\{(w_{lip}+w_{water})×i-w_{water}+r_{ax}\}^2 ]×l\qquad(3)$$ $$MLV=∑_{i=0}^{2n}π[\{(w_{lip}+w_{water})×i+w_{lip}+r_{ax}\}^2-\{(w_{lip}+w_{water})×i+r_{ax}\}^2 ]×l\qquad(4)$$ where $w_{lip}$ and $w_{water}\:$ represent the thickness of the lipid layer and water layer, and $r_{ax}$ is the inner radius of the axon (Fig. 1a). Then, $κ_{my}$ is expressed as $$κ_{my}=\frac{MWV}{MWV+MLV}=\frac{w_{water}}{(1+\frac{1}{2n})w_{lip}+w_{water}}.\qquad(5)$$ In axon and extracellular compartments, their MR-visible and MR-invisible volumes were calculated using their mass and density measurements. Assuming that the two compartments have the same ratio, ⁴ axonal&extracellular water volume (AWV) and axonal&extracellular non-water volume (ANWV) are expressed as $$AWV=m_{ax\&ex\_water}/ρ_{ax\&ex\_water}\qquad(6)$$ $$ANWV=m_{ax\&ex\_non-water}/ρ_{ax\&ex\_non-water}\qquad(7)$$ where $m$ and $ρ$ represent the mass and density, respectively. Then, $κ_{ax}$ and $κ_{ex}$ are obtained using $$κ_{ax}=κ_{ex}=\frac{AWV}{AWV+ANWV}.\qquad(8)$$

[Parameters of scaling factors] All parameters for scaling process were from literature values of mammalian CNS. For $κ_{my}$, $w_{lip}$ and $w_{water}$ were set to be 51Å and 29Å, respectively.⁵ For $κ_{ax}$ and $κ_{ex}$, $m_{ax\&ex\_water}=0.638g/gWM$, $m_{ax\&ex\_non-water}=0.14g/gWM$, $ρ_{ax\&ex\_water}=1g/ml$, and $ρ_{ax\&ex\_non-water}=1.33g/ml$ were used (gWM:1g of white matter).⁶

[Validation] To validate the scaling factors, an existing histo-imaging dataset was utilized.⁷ The dataset contained histologically measured MVF (MVF_HIST) and MR-measured MWF from MWI. Using the proposed scaling factors, we translated MR-measured MWF into MVF (MVF_MRI). Then, MVF_MRI and MVF_HIST were compared.³

[Experiment] MWF was estimated by using multi-echo gradient-echo (GRE) MWI described in Jung et al.³ Then, MWF was scaled to MVF using Equation (2). For axonal volume fraction (AVF), neurite density and orientation dispersion imaging (NODDI) was acquired. g-ratio was calculated using MVF and AVF maps. The scan parameters were as follows: GRE: FOV=256×208mm², TR=1400ms, TE=2.5:2.2:40ms, flip angle=83°, voxel size=2×2mm², thickness=2mm. NODDI: three-shell diffusion weighted imaging data (b=300s/mm², 700s/mm² and 2000s/mm² with 8, 32 and 64 directions, respectively; b=0s/mm² with 13 averages) were acquired using a spin-echo EPI sequence with TR/TE=4000/95ms, FOV=192×192mm², voxel size=2×2mm², thickness=2mm.

[Simulation] To investigate the robustness of the scaling factors, we performed a computer simulation. Three parameters, thickness ratio (=$w_{lip}/w_{water}$), $κ_{my}$ and $κ_{ax}$ (=$κ_{ex}$), were varied and the resulting MVF and g-ratio were calculated. The range of each parameter was based on the literature values of mammalian CNS:

• Thickness ratio: 1.5~1.8 (1.55 in rabbit optic nerve and 1.73 in rat optic nerve) ^5,8
• $κ_{my}$: 0.35~0.4 (0.36, 0.38, and 0.4) ^3,9
• $κ_{ax}$: 0.8~0.9 (0.8, 0.82, 0.86, and 0.9) ^3,9-11
  

Results

$κ_{my}$ was 0.36 when the average number of lamellae (=15) in mammalian CNS nerves ¹² was used (Fig. 1b), and $κ_{ax}$ (=$κ_{ex}$) was 0.86. When applying these scaling factors to the histo-imaging dataset, ⁷ the result showed a good correspondence between MVF_MRI and MVF_HIST with an almost perfect regression line (y=1.02x+0.016) and a high R² value (=0.69), validating the proposed scaling approach (Fig. 2a). The resulting in-vivo g-ratio map was around 0.79 in white matter as shown in Fig. 2b.

In the computer simulation, no substantial change in MVF and g-ratio was observed for the ranges of the parameter variations (Fig. 3). When the thickness ratio or $κ_{my}$ or $κ_{ax}$ was changed, the fractional variation of MVF was less than 7% and that of g-ratio value was less than 2.5%. Hence, the variations in the scaling parameters had limited influences on MVF and g-ratio values, indicating the robustness of the scaling factor.

Discussion and Conclusion

Acknowledgements

References

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