 Diffusion MRI gradient sampling

Diffusion MRI gradient sampling is the choice of magnetic field gradient directions, strengths and repetitions used to acquire diffusion magnetic resonance imaging measurements. Under a Gaussian diffusion tensor model, different directions probe different values of a quadratic form. Acquiring many measurements in an uninformative set of directions cannot determine every tensor coefficient.

For a unit gradient direction $\mathbf{g}$, a separately measured matched baseline $S_0$ and fixed positive diffusion weighting b-value $b$, the ideal signal model isThe symmetric matrix $\mathbf{D}$ has six independent coefficients. Opposite directions $\mathbf{g}$ and $-\mathbf{g}$ give the same model prediction. Thus counting orientations without considering their independent information can overstate diffusion tensor identifiability.

A 2003 Monte Carlo simulation study controlled the observation budget: one baseline plus60 diffusion-weighted observations. Six distinct orientations repeated ten times and30 distinct orientations repeated twice each use60 diffusion-weighted observations. The comparison asks how angular coverage and repetition affect estimated orientation, rather than simply comparing a longer acquisition with a shorter one.^[ref]

The subsequent 2004 study compared direction schemes through estimated orientation, trace and fractional anisotropy at $b=1000s/m{\mathrm{m}}^2$. These are distinct outputs of the same tensor fit. An acquisition suited to one readout need not minimize uncertainty in another.^[ref]

An original design comparison separates two questions. Repeating the three coordinate axes may reduce random variation in their measured attenuations, but it adds no equations for the three off-diagonal tensor entries. Adding suitable mixed directions can supply those equations. Full matrix rank establishes uniqueness in the ideal model; practical measurement uncertainty, motion and model mismatch still require assessment.