Diffusion MRI biophysics

Diffusivity-based measurements

A tensor can provide fractional anistropy (FA), axial diffusivity (AD), radial diffusivity (RD), and mean diffusivity (MD). AD, denoted by λ parallel, quantifies how fast water diffuses along the axonal fibers. It is estimated by λ1, the first eigenvalue of the tensor. RD, denoted by λ perpendicular, quantified how fast water diffuses across the axonal bundles. It is estimated by (λ2+λ3)/2, the average of the second and third eigenvalues of the tensor. MD is the diffusivity average from the three eigenvalue of the tensor. It is often regarded as an approximation of the overall ADC. FA is a fraction derived from the ratio between λ1, λ2, and λ3. It has a value ranged from 0 (isotropic) to 1(totally anisotropic).

In general, good myelinated fibers have high FA and low RD (Chang 2017). When there is demyelination, RD changes dramatically (Song, 2002). If there is axonal loss, the AD drops (Song 2003). Many studies have used RD specifically for myelination due to the demyelination studies. However, the fact that demyelination has RD change does not mean that good myelination is also reflected by RD (Change 2017). The interpretation of RD requires additional caution.


Numerous studies have investigated the relation between diffusivity and pathological conditions.
Axonal injury: AD ↓(Budde et al., 2007; Song et al., 2003)
Demyelination: RD ↑ (Budde et al., 2007; Song et al., 2002; Song et al., 2005) 
Myelination: FA  (Chang, 2017), RD (partly, Chang, 2017).
Tumor: ADC↓(Gauvain et al., 2001; Kono et al., 2001; Sugahara et al., 1999)
Immune cell infiltration: ADC↓
Vasogenic edema: ADC↑
Cytotoxic edema: ADC↓
Hemorrhage: ADC↓


Figure from Zhang, Jiangyang, Manisha Aggarwal, and Susumu Mori. "Structural insights into the rodent CNS via diffusion tensor imaging." Trends in neurosciences35.7 (2012): 412-421.

In 1990, Michael Moseley showed the clinical application of diffusivity. His study showed a decrease in water diffusion in the early phase of acute brain ischemia in a cat brain. 

Significance


1. Diffusivity provides a noninvasive way to study axonal injury, demyelination, edema...etc.

Limitation


Diffusivity inherits all limitations of a tensor model, which includes the following:

1. It assumes single fiber population. In other words, in place with crossing or branching fiber, the diffusivity measurement is not accurate.
2. Partial volume effect. Diffusivity is an overall estimation of how fast water diffuses. If fast and slow diffusion components coexist, the overall diffusivity can be increased or decreased. 

The following image show the partial volume problem in diffusivity-based measurement.
The diffusion phantom examines three types of the partial volume effect: (a) fibers/free water, (b) fibers crossing, and (c) fibers/non-diffusive materials.

The resulting FA, AD, RD, MD maps are the following


Density-based measurement


Studies have shown that QA is less susceptible to the partial volume effect:

A: FA map
B: GFA map
C: QA at horizontal
D: QA at vertical 
source: Yeh, Fang-Cheng, et al. "Deterministic diffusion fiber tracking improved by quantitative anisotropy." (2013): e80713.

Questions

1. Is diffusivity a b-value dependent measurement? How about FA?
2. What is the difference between QA and FA?
2. A study found that AD is significantly decreased in a brain region. What would be the possible explanation for the change? How about FA, RD, ADC?

Exercise

1. Use voxel-based analysis to obtain mean FA, ADC, MD, RD of the corpus callosum (follow instructions in How to analyze diffusion data?)
2. Manually rotate the SRC file (instructions in Reconstruction(DTI, QBI, DSI, GQI, QSDR)) and repeat the VBA analysis. Do those diffusion indices change due to the rotation?

Reference

[1] Beaulieu, C., 2002. The basis of anisotropic water diffusion in the nervous system - a technical review. NMR Biomed 15, 435-455.
[2] Budde, M.D., Kim, J.H., Liang, H.F., Schmidt, R.E., Russell, J.H., Cross, A.H., Song, S.K., 2007. Toward accurate diagnosis of white matter pathology using diffusion tensor imaging. Magn Reson Med 57, 688-695.
[3] Gauvain, K.M., McKinstry, R.C., Mukherjee, P., Perry, A., Neil, J.J., Kaufman, B.A., Hayashi, R.J., 2001. Evaluating pediatric brain tumor cellularity with diffusion-tensor imaging. AJR Am J Roentgenol 177, 449-454.
[3] Kono, K., Inoue, Y., Nakayama, K., Shakudo, M., Morino, M., Ohata, K., Wakasa, K., Yamada, R., 2001. The role of diffusion-weighted imaging in patients with brain tumors. AJNR Am J Neuroradiol 22, 1081-1088.
[4] Song, S.K., Sun, S.W., Ju, W.K., Lin, S.J., Cross, A.H., Neufeld, A.H., 2003. Diffusion tensor imaging detects and differentiates axon and myelin degeneration in mouse optic nerve after retinal ischemia. Neuroimage 20, 1714-1722.
[5] Song, S.K., Sun, S.W., Ramsbottom, M.J., Chang, C., Russell, J., Cross, A.H., 2002. Dysmyelination revealed through MRI as increased radial (but unchanged axial) diffusion of water. Neuroimage 17, 1429-1436.
[6] Song, S.K., Yoshino, J., Le, T.Q., Lin, S.J., Sun, S.W., Cross, A.H., Armstrong, R.C., 2005. Demyelination increases radial diffusivity in corpus callosum of mouse brain. Neuroimage 26, 132-140.
[7] Sugahara, T., Korogi, Y., Kochi, M., Ikushima, I., Shigematu, Y., Hirai, T., Okuda, T., Liang, L., Ge, Y., Komohara, Y., Ushio, Y., Takahashi, M., 1999. Usefulness of diffusion-weighted MRI with echo-planar technique in the evaluation of cellularity in gliomas. J Magn Reson Imaging 9, 53-60.

[8] Chang, E. H., et al. (2017). "The role of myelination in measures of white matter integrity: Combination of diffusion tensor imaging and two-photon microscopy of CLARITY intact brains." Neuroimage 147: 253-261.


Comments