13 Computational Biomechanics of the Brain in the Operating Theatre
337
violation of the constraint remains along that direction. However, the initial point
can end up anywhere on the plane orthogonal to n i , not necessarily on its initial
projection. Note that bounding λ forces may break that condition, in case of very
large (mis)pairing distances. The shift in the orthogonal direction is given by the
constraint solver minimising the energy necessary to satisfy the set of constraints.
Depending on the type of elements, the sliding constraints are defined along the
following directions:
• a projection on a plane yields to a single constraint along direction n 1 . The point
can slide along this plane: after resolution, it will be located on the plane, but not
necessarily on its initial projection.
• a projection on a line segment yields two constraints along n 1 and n 2 . The point
can slide along this line: after resolution, it will be located on the line, but not
necessarily on its initial projection.
An example of sliding constraint is given in Fig. 13.5. For an iteration k of the
registration method, each point can slide along its segment of projections. Its final
position depends on all other constraints applied to the model. The next iteration(s)
will then enable the convergence towards a local solution.
Advantages of using the sliding constraints in an iterative registration process are
then:
• no a priori information is required during the pairing step. Closest projections
only are used, plus the filtering step.
• in the case of mispairings, for example, projection of a point onto the wrong
vessel, the considered point will end up far from its initial target projection, if
other better-suited constraints force the model into another direction.
• in the case of antagonist constraints, none or few of them should be resolved, and
a new iteration will occur.
• at each new iteration k, pairings will be redefined. The expected behaviour is
that the uncertainty of the pairings will decrease as long as the process converges
towards an overall acceptable solution.
13.3.5 Clinical Evaluation
As presented in [8], our method has been evaluated on five retrospective cases.
Data were collected by the SINTEF Medical Technology Institute at St. Olav’s
University Hospital (Trondheim, Norway) [38]. For each clinical case, T2-FLAIR
and angiographic MRI images were acquired before surgery. During the procedure,
ultrasound images were acquired with the navigation system SonoWand [39]. These
data were collected through a clinical study approved by the local ethics committees,
and the consent of each patient was obtained prior to the procedure.
337
violation of the constraint remains along that direction. However, the initial point
can end up anywhere on the plane orthogonal to n i , not necessarily on its initial
projection. Note that bounding λ forces may break that condition, in case of very
large (mis)pairing distances. The shift in the orthogonal direction is given by the
constraint solver minimising the energy necessary to satisfy the set of constraints.
Depending on the type of elements, the sliding constraints are defined along the
following directions:
• a projection on a plane yields to a single constraint along direction n 1 . The point
can slide along this plane: after resolution, it will be located on the plane, but not
necessarily on its initial projection.
• a projection on a line segment yields two constraints along n 1 and n 2 . The point
can slide along this line: after resolution, it will be located on the line, but not
necessarily on its initial projection.
An example of sliding constraint is given in Fig. 13.5. For an iteration k of the
registration method, each point can slide along its segment of projections. Its final
position depends on all other constraints applied to the model. The next iteration(s)
will then enable the convergence towards a local solution.
Advantages of using the sliding constraints in an iterative registration process are
then:
• no a priori information is required during the pairing step. Closest projections
only are used, plus the filtering step.
• in the case of mispairings, for example, projection of a point onto the wrong
vessel, the considered point will end up far from its initial target projection, if
other better-suited constraints force the model into another direction.
• in the case of antagonist constraints, none or few of them should be resolved, and
a new iteration will occur.
• at each new iteration k, pairings will be redefined. The expected behaviour is
that the uncertainty of the pairings will decrease as long as the process converges
towards an overall acceptable solution.
13.3.5 Clinical Evaluation
As presented in [8], our method has been evaluated on five retrospective cases.
Data were collected by the SINTEF Medical Technology Institute at St. Olav’s
University Hospital (Trondheim, Norway) [38]. For each clinical case, T2-FLAIR
and angiographic MRI images were acquired before surgery. During the procedure,
ultrasound images were acquired with the navigation system SonoWand [39]. These
data were collected through a clinical study approved by the local ethics committees,
and the consent of each patient was obtained prior to the procedure.