Fuzzy Fibers: Uncertainty in dMRI Tractography - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 83

8.4 Perspectives

8.4.1 Evidence for Model Selection

Many of the methods for finding per-voxel fiber count (or more generally the per-
voxel signal model) described in Sect. 8.3.2 share two notable properties which may
be reconsidered and relaxed in future research. First, they deterministically calculate
the single best model, with hard transitions between the regions best explained by
one model versus another [ 1 , 17 , 26 , 50 , 56 , 58 ]. Yet we know that partial voluming
(Sect. 8.3.3 ) creates smooth transitions between different neuroanatomic tissue
regions. Though computational expensive, Markov Chain Monte Carlo (MCMC)
sampling of both model parameter space and the set of models enables averaging
information from more than one model [ 2 , 8 ]. Second, most methods work within
a particular hierarchical set of linearly ordered models (SH of different orders [ 1 ],
ball and multiple sticks [ 2 ], sum of higher-order rank-1 terms [ 58 ]). One can easily
imagine configurations, however, that confound such a linear ordering: an equal mix
of two fibers crossing and isotropic diffusion (perhaps due to edema), or a mix of
one strong fiber and two weaker equal-strength fibers. Furthermore, there is rarely
objective comparison or reconciliation between disjoint sets of models.
An informative perspective on these situations may be gained by directly visual-
izing, either on data slices or by some form of volume rendering, the fitness of a large
palette of possible models. In a Bayesian setting, the model fitness can be quantified
by the marginal likelihood of the data x given the model M k , or the model evidence ,
computed by integrating over the model parameter space θ k [ 36 ].

P

evidence =

( x | M k ) P ( x | θ k , M k ) P ( θ k | M k ) d θ . (8.1)

likelihood prior

Bretthorst et al. [ 8 ] have pioneered the calculation and visualization of model
evidence for dMRI, but many possible directions are left unexplored, including the
application to counting fibers, and to models that account for intra-voxel fanning or
bending [ 41 ].

8.4.2 Reproducibility, Seeding, and Preprocessing

The reproducibility of tractography depends on many factors. The manual placement
of seed points is an obvious concern. Detailed written instructions improve repro-
ducibility between operators [ 13 ], especially across sites [ 65 ]. Combining multiple
seed regions with logical operators makes the results more reproducible [ 21 , 24 ] and
seeding protocols for up to 11 major fiber bundles have been developed this way [ 65 ].
Warping individual brains to a standard template has also been reported to increase