Importance of exactb-tensor calculation for quantitative diffusion tensor imaging and tracking of neuronal fiber bundles

Abstract

Abstraer. Quantitative diffusion tensor imaging (DTI) is a novel method of magnetic resonance (MR) imaging providing information on the brain's microstructure in vivo. DTI can be effectively measured with modern clinical MR scanners. However, imaging sequence details required for accurate b matrix calculation and for following DTI quantification ate normally unknown to the user. In this work, we investigated the accuracy of b value approximation ir the b matrix is calculated without taking into account the effect of imaging gradients. It was found that an error of more than 4% in DTI estimation arises for a quite typical brain imaging protocol. The errors in mean diffusivity and fractional anisotropy index depend on diffusion tensor shape and eigenvectors orientation and exceed noise level in DTI quantification. These errors however have a strong impact on fiber tracking -up to 30% difference was found between the fiber tracks corresponding to exact and approximate calculated DTI data. Since these errors are dependent on imaging parameters and sequence implementation, accurate b matrix calculations are important for adequate comparison between data acquired on different MR scanners and also for data measured with the different imaging protocols.

Physical foundations, models, and methods of diffusion magnetic resonance imaging of the brain: A review

“…Equation [44] establishes a relationship between the diffusion-weighted signal s and the diffusion tensor D, but leaves the problem of how D can be measured in an MRI experiment. The solution put forward by Stejskal in 1965 is not applicable in its original form, because it is for the laboratory frame of reference, and in an MRI experiment the reference frame of the diffusion tensor in each voxel is not known a priori, and the sample cannot be reoriented in the magnet (2).…”

“…Analytical expressions for the b-matrix can be derived for a given pulse sequence: a method of derivation can be found in (30). Notwithstanding the resulting limitation on accuracy, the effect of imaging and spoiling gradients is often neglected because their strength is typically small compared to that of the diffusion-weighting gradients, simplifying calculations by enabling to use the scalar b-factor b ¼ b xx þ b yy þ b zz (44). A geometrical method for computing the b-value and an analogy for the effect of cross terms can be found in Ref.…”

“…A geometrical method for computing the b-value and an analogy for the effect of cross terms can be found in Ref. (44).…”

“…Equation [42] can be rewritten as s ¼ expðÀbu T DuÞ; [44] where u is the unit vector corresponding to the direction of the diffusion-sensitizing gradient, and the nor- For a PGSE sequence, from Eq. [43] we obtain…”

Quantitative diffusion tensor MR imaging of the brain: field strength related variance of apparent diffusion coefficient (ADC) and fractional anisotropy (FA) scalars

“…The effect of changes in the duration, amplitude and separation of the diffusion gradients on the b-value was controlled by an accurate b-matrix calculation. The b-matrix was calculated numerically on the basis of the exact gradient shapes of all gradients (diffusion encoding and imaging gradients) [30]. The b-matrix changed slightly, which was taken into account in the calculations.…”