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Image-guided neurosurgery based on navigation systems has been developed to assist
intracranial tumor resection surgery. The success of the surgery relies heavily on the
precision of the navigation system, which decreases due to a phenomenon called "brain
shift". During craniotomies, the soft tissues of the brain deform due to gravitational
force, cerebro spinal fluid leakage, intracranial pressure change or surgical interventions.
This significantly deteriorates the assumption of linear geometrical differences
between pre-operative and intra-operative images. To compensate for such non-linear
deformations, non-rigid registration techniques are employed.
The first contribution of this PhD work is the development of a new approach for
inter-subject non-rigid registration of 3D magnetic resonance (MR) brain images. It is
motivated by the ideas derived from elastodynamics which is the subclass of linear elastic
theory. We proposed to model the non-rigid deformations as elastic waves which
are characterized by elastodynamics wave equation. The registration process ensues
in a hierarchical fashion, thus reducing the risk of obtaining a local optimal transformation.
Experimental results demonstrated that the proposed deformable registration
method leads to very promising results when applied to the problem of inter-subject
registration and that favorably compared against classical registration approaches.
The second contribution of this work is the incorporation of topology preservation
property into our proposed inter-subject non-rigid registration method. We proposed
to impose the topology preserving penalty on the deformation by constraining the Jacobian
determinant of the transformation to be positive over the entire image domain.
This property ensured that the recovered transformations do not exhibit tearing or folding effects. The results of the proposed registration approach were compared in terms
of Kappa index and relative overlap over segmented anatomical structures to that obtained
with existing topology preserving non-rigid image registration methods and non
topology preserving variant of our proposed registration scheme. The Jacobian determinant
maps obtained with our proposed registration method were qualitatively and
quantitatively analyzed. The results demonstrated that the proposed scheme provides
good registration accuracy and results into smooth transformation with a guarantee to
preserve topology.
The third contribution of this PhD work is that we developed a new inverse consistent
non-rigid image registration method based on elastodynamics. Inverse consistency
property renders the registration procedure unbiased towards the order of input images.
This assures that the forward and reverse transformations are inverses of each
other which do not change by switching the input images. We introduced the inverse
consistency constraint into the inertial force that is part of the elastodynamics wave
equation which governs the underlying non-rigid deformations. We conducted image
registration experiments, with and without inverse consistency constraint, on three different
datasets comprising of 3D MR brain scans. The extent to which the proposed
registration scheme enforced inverse consistency was analyzed through inverse consistency
error. The results revealed that the inverse consistency error reduced by 99%
with our inverse consistent registration method as compared to the non-inverse consistent
counterpart. Thus, the proposed inverse consistent registration method seems very
promising both in terms of registration accuracy and inverse consistency error.