Fuzzy Fibers: Uncertainty in dMRI Tractography - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 81

8.3.2 Model Uncertainty and Selection
Methods for tractography that seek to recover more than a single fiber direction in a
given area have tomake a judgement about howmany fiber directions can bemeaning-
fully recovered from the dMRI data. The combination of measurement noise, partial
voluming, and the practical constraints on howmany diffusion weighted images may
be acquired create uncertainty in the number of fibers present. Qualitatively different
than the angular uncertainty in a single fiber direction, the traditional focus of prob-
abilistic tractography, this uncertainty can be a viewed as a kind of model selection
uncertainty , which is described further in Sect. 8.4.1 .
Uncertainty in fiber number has been handled by different tests that either sta-
tistically sample or deterministically choose a level of model complexity (with an
associated fiber number) froma nested set of models. Behrens et al. [ 2 ] use Automatic
Relevance Determination (ARD) to probabilistically decide the number of “sticks”
(fibers) in their ball-and-multiple-stick model. Within their probabilistic tractogra-
phy, this achieves Bayesian Model Averaging [ 22 ] of the fiber orientation. For deter-
ministic tractography, Qazi et al. [ 50 ] use a threshold on the (single, second-order)
tensor planarity index c p [ 66 ] to determine whether to fit to the diffusion weightes
images a constrained two-tensor model [ 46 ] that permits tracing two crossing fibers.
Schultz et al. compare different strategies for deciding the appropriate number
of fiber compartments, based on the diminishing approximation error [ 56 ], thresh-
olding compartment fraction coefficients of a multi-fiber model [ 58 ], or by learning
the number of fiber compartments using simulated data and support vector regres-
sion [ 54 ], which represents uncertainty in the form of continuous estimates of fiber
number (cf. Fig. 8.5 ).
Much of the work on determining the number of per-voxel fiber components has
been described outside of any particular tractography method, but may nonetheless
inform tractographic analysis. Alexander et al. [ 1 ] use an F-Test to find an appropri-
ate order of Spherical Harmonic (SH) representation of the ADC profile. Jeurissen
et al. [ 26 ] decide the number of fibers by counting significant maxima in the fiber
orientation distribution after applying the SH deconvolution (constrained by posi-
tivity) of Tournier et al. [ 62 ]. The SH deconvolution of Tournier et al. [ 62 ]insome
sense involves model selection, because the deconvolution kernel is modeled by the
Fig. 8.5 Support vector
regression estimates the
number of fiber compartments
per voxel as a continuous
quantity, indicating regions in
which a discrete number of
fiber compartments can only
be determined with
considerable uncertainty [ 54 ]