maryam afzali1, Sharlene Newman1, Eleftherios Garyfallidis2, and Hu Cheng1
1Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, United States, 2Department of Intelligent Systems Engineering, Indiana University, Bloomington, IN, United States
Synopsis
We showed that
three shells are sufficient to result in good approximations of MAP-MRI indices
from numerical simulation. We used multiple compartment microstructure models to
fit the two shell data and extrapolate the third shell with a higher b-value.
We compared the performance of two models, NODDI and NODDI with fiber crossing
(NODDIx), on the Human Connectome Project (HCP) DWI data. NODDIx showed
improvement in the white matter with extrapolation but NODDI did not. Both
NODDI and NODDIx failed to improve the results in the gray matter. Our approach
also provides a new mechanism in validating or comparing microstructure models.
Introduction
Diffusion weighted imaging (DWI) has been a great
non-invasive method for investigating brain microstructure1.
Most DWI based analysis of the microstructure fall into two categories: model
of the tissue to acquire tissue-specific metrics and model of the signal to
compute quantitative physical properties of the diffusion2.
Recently, a signal-based framework called Mean
Apparent Propagator (MAP)-MRI uses a series of basis functions to fit the
three-dimensional q-space signal and transform it into diffusion propagators3. The
advantage of MAP-MRI is that it is essentially model-free. MAP-MRI provides richer information of microstructural features
compared with DTI-derived indices.
The motivation of this work is to use
two-shell data to predict the third shell and use these data to derive more
microstructure information in the framework of MAP-MRI. In this work, we first
showed that three shells can give reasonable results as compared to 6 shells
from numerical simulation. Then we proposed an extrapolation method based on
NODDI4 and an extended NODDI model with fiber
crossing (NODDIx)5 on the Human
Connectome Project (HCP) data (3 shells). We compared the MAP-MRI indices from
extrapolated results and the original ones. Methods
The general
framework of extrapolation and MAP-MRI is illustrated in Fig. 1. Six MAP-MRI indices were computed: the return-to-origin probability
(RTOP),
and its projection to the diffusion tensor axis and perpendicular plane: RTAP and RTPP; the non-Gaussianity
(NG) index, and the projection of NG to the diffusion
tensor axis and perpendicular plane NGpar and NGper.
We generated the synthetic diffusion signals using the MAP-MRI framework with b-value = [1000,
2000, 3000, 4000, 5000, 6000] s/mm2, and the same b-vectors as used
in the HCP protocol for each shell. We generated three sets of data (each contained 100 voxels) to
represent different WM regions using the MAP coefficients and scaling factors
derived from three white matter voxels of one HCP subject. The scaling factor for data 1, data 2, and data 3 were [0.0103, 0.0043, 0.0033],
[0.0082, 0.0056, 0.0051], [0.0074, 0.0068, 0.0053] respectively. The SNR was
set to 20.
The extrapolation was performed on the two inner shell data based on NODDI
and NODDIx models. The MAP-MRI indices were calculated from two shells data (b
= 1000, 2000), three shells data (b = 1000, 2000, 3000), all six shell data,
and the two shell data plus the extrapolated third shell (b = 3000) using NODDI
and NODDIx. These datasets were denoted as 2-shell, 3-shell, 6-shell, 2-shell+
NODDI, and 2-shell+ NODDIx DWI data. Root Mean Square Error (RMSE) was computed
for MAP-MRI indices with respect to the true values.
To test the extrapolation on human subjects, we used DWI data of 10 subjects
from the HCP dataset. The MAP-MRI indices
were calculated from two shell data (b = 1000, 2000), original three shell data
(b = 1000, 2000, 3000) and the two shell data plus the extrapolated third shell
(b = 3000) using NODDI and NODDIx. Root Mean Square Error (RMSE) was computed by using the original 3-shell data as ground truth.
Results
The results from the numerical simulation are summarized in Table 1.
Results with 3 shells were most comparable with 6-shell results.
In all cases except NGpar of the corpus callosum voxel, the
results of extrapolation with NODDIx were all better than those with 2-shell
data.
Figure 2 shows the human results. Using two shells of the DWI data
could result in moderate differences from the 3-shell data. Extrapolation using
NODDI did not improve the results. In contrast, extrapolation with NODDIx
showed promising improvements from two shell results in the white matter (WM)
region, in which extrapolation with NODDIx is superior to two-shell data or
extrapolation with NODDI for all MAP-MRI metrics. However, in the gray matter
(GM) region, both extrapolation with NODDI and NODDIx yielded larger error than
2-shell data.
The ratio of RMSE over mean value of MAP-MRI indices using different methods for 10 HCP subjects is shown in Fig. 3. First of all, the rank of these three methods was very
consistent across subjects. Second, without surprise, 2-shell+ NODDIx scored
the smallest error across all six indices for most subjects. Discussions
We have demonstrated from numerical simulation that using three shells with
b-value from 1000 – 3000 s/mm2 can result in better approximation
for MAP-MRI metrics than two shell data. We found
that extrapolation with NODDIx improved the accuracy of the MAP-MRI metrics in
the white matter while extrapolation with NODDI did not. This new technique can
be applied to existing DWI data with two shells to perform MAP-MRI analysis in
addition to NODDI and DKI. Acknowledgements
The
authors would like to thank Evren Özarslan, PhD, for providing a data with all
MAP-MRI parameters as ground truth which made the implementation of his method
easier.References
1.Basser,
P.J., Mattiello,
J., LeBihan,
D., 1994b. MR diffusion tensor spectroscopy and imaging. Biophys.
J. 66, 259-267.
2.Ferizi,
U.
et al., 2016.
Diffusion MRI microstructure models with in vivo human brain Connectom
data: results from a multi-group comparison. arXiv:1604.07287 [physics.med-ph].
3.Özarslan,
E.
et al., 2013.
Mean apparent propagator (MAP) MRI: A novel diffusion imagingmethod
for mapping tissue microstructure.
4.Zhang,
H.
et al., 2012.
NODDI: Practical in vivo neurite orientation dispersion and density imaging of
the human brain. Neuroimage
61, 1000-1016.
5.Farooq,
H.
et al., 2016.
Microstructure Imaging of Crossing (MIX) White Matter Fibers from diffusion
MRI. Sci
Rep, 38927.