Diffusion MRI Metrics


Introduction: GQI versus DTI


A common question for GQI users is "how does GQI differ from DTI?" and "What are the differences between QA and FA?" The following are several highlights. A PowerPoint slide is also available at the bottom of the page if you would like to include in your presentation.

Restricted diffusion versus overall diffusion


The DTI model does not (or not able to) specify restricted diffusion contributed by axonal myelination. The consequence is that FA, AD, MD will reflect a portfolio of biological changes including edema, inflammation, or just a superimposing crossing fiber (see  Yeh F-C et al. PLoS ONE 8(11): e80713.2013). Using DTI metrics will results in a large variation due to the complexity of the real world biological changes, and often time a large sample size is needed to find statistical significance.

GQI has a length parameter (termed diffusion sampling lengh ratio) to specify the distance scale for restricted diffusion to be evaluated. As a result, QA is quantifying the anisotropy of restricted diffusion and thus more robust against inflammation and edema. A neurosurgery study has shown that QA is robust against peritumoral edema and contributes to more reliable tractography (Zhang, et al. Neurosurgery, 73(6), 1044-1053. 2013). 

Diffusion rate versus diffusion density


All tensor derived measurements, including FA, AD, RD, are based on "diffusivity", which by definition measures the "rate" of diffusion. The biggest drawback of using diffusivity is that none-restricted and restricted diffusion are always mixed due to Brownian motion. Separating them will require complicated model fitting (e.g., fitting multiple tensor) and usually does not work well for low SNR data (common in high b-value acquisitions).

In comparison, GQI and QSDR quantifies diffusion "density". They are based on the q-space imaging to quantify the density of restricted and less-restricted diffusion. The separation of restricted and less-restricted diffusion can be readily achieved in an simple analytical linear relation. The performance is better than DTI in low SNR condition. The derived metrics (e.g. QA, ISO) is measuring the density of diffusing water, and thus QA is measuring the density of anisotropic diffusing water.

Fiber-specific versus voxel-based


QA quantified anisotropy for each fiber population, whereas FA is shared by all fiber population within a voxel. QA is a fiber-specific measurement and defined per fiber population and thus offers a measurement for each of them. By contrast, FA is defined per voxel, and all fiber populations within a voxel will share the same measurement. If there are crossing fibers, FA will decrease, whereas QA is less affected.

Sensitivity to physiological differences


In application, diffusivity measurements such as FA/AD/RD/MD are more sensitive to pathological conditions, whereas density measurements such as QA/ISO/RDI 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, while 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 that diffusivity measures such as FA 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↓

Abbreviations:

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.

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.

QA versus FA


QA measures the spin density of anisotropy diffusion along a fiber pathway. In voxels with more than one fiber populations, each one will have its QA measured independently. QA is different from diffusivity-based measurements such as FA, ADC, RD in that diffusivity measures the "rate" of diffusion (how fast water diffuses), whereas QA measures the "amount" of diffusing water using the Fourier relation of the "q-space imaging". This measurement of QA is based on a model-free nonparametric method to quantify diffusion distribution. In comparison. FA is derived from diffusivities measured in the diffusion tensor model.

Studies have compared the performance between FA and QA. A phantom study has shown that QA is more robust to free water effect and partial volume of crossing fibers. (Yeh, PloS one 8.11, 2013). A clinical case-based study has shown that QA-based tractography is more robust against peritumoral edema. (Zhang ,Neurosurgery 73.6 (2013): 1044-1053.) A more recent study (Yeh, PLoS computational biology 12.11, 2016).showed that SDF provides a unique structural characterization that can reliably identify individuals (termed local connectome fingerprint). Its reproducibility and uniqueness is higher than diffusivity-based measurements. 

It is noteworthy that since SDF reveals high individuality, the inter-subject variance of SDF can be very high (this does not mean that SDF is unreliable). As a result, connectometry is most suitable for a longitudinal study, though a cross-sectional study can also be benefited by connectometry analysis.

ć
Fang-Cheng Yeh,
Nov 7, 2019, 6:47 AM
Comments