Diffusion MRI Indices


A common question about diffusion indices is that how do they differ in term of their biophysical meaning? Here is a brief explanation. First of all, all tensor derived measurements, including FA, AD, RD, are based on "diffusivity", which by definition measures how fast water diffuses. By contrast, measurements derived from GQI or QSDR, such as QA, iso, RDI, and local connectome fingerprint are based on "density", which by definition measure how much water diffuses in a particular direction. These are two different approaches to measure the diffusion. If we compare diffusion to traffic, one way to quantify traffic is to measure how fast vehicles travels on the highway (diffusivity), and another way is to count how many vehicles are traveling (density). These measurement may be related, but entirely different in terms of their physical meanings.

In application, diffusivity measurements are more sensitive to pathological conditions, whereas density measurements are more sensitive to individual/physiological difference (see Yeh et al. PLoS Comput Biol 12(11): e1005203, where local connectome fingerprint is a type of density measurement). To better understand this difference, we can compare axons to water pipes. If the pipes are in good condition, they will have similar water transfusion rate (diffusivity will remain similar), even though the amount of water (density) being transfused can vary a lot. This indicates that diffusivity is good for detecting whether the structural is still intact, whereas the density measurement is good for quantifying the "connectivity" because it quantifies the total quantity of the diffusing water. Under this paradigm, we can figure out diffusivity measures may not vary a lot between subjects, whereas density measures will differ substantially. This is shown in Yeh et al. PLoS Comput Biol 12(11): e1005203. 
where the individuality can be better characterized by density-based measurements, not diffusivity measurements. 

DTI measures

A diffusion tensor can provide fractional anisotropy (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 citing 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.

GFA is calculated from an ODF function. The definition is documented in the q-ball imaging paper [3]. GFA has a high correlation with FA (Fritzsche, K. H., et al. (2010). Neuroimage 51(1): 242-251.), and it also suffers from the same partial volume effect as FA. The value deceases in fiber crossing or voxels with CSF partial volume. GFA values may not be comparable across different reconstruction methods since the sharpness of ODF may differ due to the reconstruction method used. It may not be comparable if different b-value and diffusion sampling scheme are used. Studies using GFA should be conducted in a careful control manner to make sure that the results are not due to other confounding factors.

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↓


fa: fractional anisotropy 
ad: axial diffusivity 
rd: radial diffusivity (the average of two radial eigenvalues) 
md: mean diffusivity (the average of all eigen values). The diffusivity (either RD, MD, or AD) calculated in DSI Studio has a unit of 10-3 mm2/s. 
txx, txy, txz, tyy, tyz, tzz the 6 entry of the tensor matrix.

GQI measures

GQI provides QA and ISO. QA is calculated from the peak orientations on a spin distribution function (SDF). Each peak orientation defines a QA value. The definition for QA is defined in the generalized q-sampling imaging paper [9]. One should note that QA is defined for each fiber orientation, whereas FA and GFA are defined for each voxel. This forms a big difference in fiber tracking, since QA can be used to filter out false fibers in crossing fiber scenario. 

QA scales with spin density and MRI signals and thus it has "arbitrary unit". This causes consistency problem in comparing QA values between scans. DSI Studio has adopts several strategies to calibrate QA , but sometimes the calibration may not be accurate enough, causing a large variability in QA. A solution to this problem is to scales the maximum QA value of a subject to 1 so that QA may be more comparable across the subject. This gives "NQA". NQA assumes that all subjects share the same compactness of the white matter bundle.

The isotropic value of the ODF [9], termed "ISO", is the minimum distribution value of an ODF. It represent background isotropic diffusion contributed from CSF or non-directional restricted diffusion (e.g. diffusion within or between cells). In multi-shell scheme, ISO is more correlated with restricted non-directional diffusion because of the higher b-value weighting, whereas in grid scheme, ISO has more weighting from free water diffusion. To separate restricted iso from non-restsricted iso, GQI has a derived method called "restricted diffusion imaging" (RDI), which provides a spectrum of RDI measures estimating restricted or non-restricted diffusion.

DSI abbreviations:
qa: quantitative anisotropy (QA). qa0 represents the QA value for the most prominent fiber orientations, and qa1 the second, ...etc. 
iso: isotropic diffusion component
nqa: normalized QA. 
rdi, nrdi: an index quantifying the density of restricted diffusion given a displacement distance (L). nRDI quantifies non-restricted diffusion. See the "restricted diffusion imaging" reconstruction above for detail.

FA versus QA

FA can be affected by several biological factors, and thus its change/pattern is more intractable. The FA will drop if there is an axonal loss, demyelination, edema, or inflammation. Thus it can be within a short time if the damage is substantial or takes longer if repeated inflammation causes a long-term neuronal loss. The timescale can be as short as few hours(edema) to one month (inflammation) or even take up to several months (axonal loss). The change of FA can be reversed if it is due to inflammation and edema without demyelination. 

QA is more robust because it is less affected by the inflammation and edema (see:  Zhang, et al. Neurosurgery, 73(6), 1044-1053. 2013). It is because there is separate metric called "iso" extracted from the calculation to model edema. QA will be more specific to neural change itself. 

QA scales with spin density. These features make it less susceptible to partial volume effect (see a comparison in Yeh F-C et al. PLoS ONE 8(11): e80713.2013). However, since QA scales with spin density, it is affected by T2-shine through, receiver gain, and B1 inhomogeneity. The QA value may not be comparable across subject if different TE and diffusion sampling scheme are used.

QA scales with diffusion signals and thus can be affected by the gain of the receiver coil. To ensure a better consistency/reproducibility, DSI Studio uses a voxel with free water diffusion to calibrate QA. The "CSF calibration" option use spatial normalization to search for voxels in the 3rd ventricle and use it to calibrate QA and achieve better reproducibility.