From Diffusion MRI to Brain Connectomics - Modeling in Computational Biology and Biomedicine - page 215

Fig. 6.10 Deterministic Tractography on ODFs. ( a ) Three fiber bundles are traced, starting from
different seed regions. Red : seeds in the CC ( left-right ). Blue : seeds in the CST (superio-inferior).
Green : seeds in the SLF (anterio-posterior). ( b ) Zoom into crossing region

Finally, for stopping they proposed four criteria—the tracts are within the image
volume, the tracts are in regions with FA value higher than a threshold, the curvature
of a tract is smaller than a threshold, and that a tract is better aligned with the major
eigenvector in the next spatial location than any of the two other eigenvectors.
The streamline tractography algorithm can be adapted to SDFs with multiple
maxima (EAP/ODF etc.) by modifying Eq. ( 6.33 )to

d r )

ds =

( s

η θ min ( r ( s )) , r (0) = η max (0) , (6.34)

where η i ( , η max is the unit

maximum vector whose function value is the largest amongst all the η i ,and η θ min
is the unit maximum vector in the current step that is most collinear to the unit
maximum vector followed by the integration in the previous step. Equation ( 6.34 )
and the initial condition state that at the starting point the integrating begins along
the dominant maximum direction, and at each consecutive step first all the maxima
of the SDF are detected and the maximum direction most collinear to the maximum
direction from the previous integration step is chosen to move forward in the
integration (Fig. 6.10 ).
The maximum direction most collinear to the previously chosen maximum
direction can be chosen by computing the dot product between the previously
chosen maximum direction and all the maxima of the current step, and by
considering the absolute values of the dot products. Hence, the maximum chosen
for the next integration direction is the maximum whose absolute value of its dot
product with the previously chosen maximum direction is the largest. Also to avoid
erratic forward and backward steps during the integration, if the value of the dot
product is negative, it is necessary to flip the unit maximum direction to point it
consistently along the fiber direction, just like in [ 7 ].
Since streamline tractography requires a continuous field of SDFs for integrating
Eq. ( 6.34 ), a continuous field of SDFs can be computed from a simple Euclidean
interpolation of the SDFs when the SDFs are expressed in the SH basis. The

r ( s )) are all the unit maxima vectors of the SDF at r ( s )