This contribution presents finite element computation of the deformation field within the brain during craniotomy-induced brain shift. The results were used to illustrate the capabilities of non-linear (i.e. accounting for both geometric and material non-linearities) finite element analysis in non-rigid registration of pre- and intra-operative magnetic resonance images of the brain. We used patient-specific hexahedron-dominant finite element mesh, together with realistic material properties for the brain tissue and appropriate contact conditions at boundaries. The model was loaded by the enforced motion of nodes (i.e. through prescribed motion of a boundary) at the brain surface in the craniotomy area. We suggest using explicit time-integration scheme for discretised equations of motion, as the computational times are much shorter and accuracy, for practical purposes, the same as in the case of implicit integration schemes. Application of the computed deformation field to register (i.e. align) the pre-operative images with the intra-operative ones indicated that the model very accurately predicts the displacements of the tumour and the lateral ventricles even for limited information about the brain surface deformation. The prediction accuracy improves when information about deformation of not only exposed (during craniotomy) but also unexposed parts of the brain surface is used when prescribing loading. However, it appears that the accuracy achieved using information only about the deformation of the exposed surface, that can be determined without intra-operative imaging, is acceptable. The presented results show that non-linear biomechanical models can complement medical image processing techniques when conducting non-rigid registration. Important advantage of such models over the previously used linear ones is that they do not require unrealistic assumptions that brain deformations are infinitesimally small and brain stress-strain relationship is linear.

Both post-mortem and neuroimaging studies have contributed significantly to what we know about the brain and schizophrenia. MRI studies of volumetric reduction in several brain regions in schizophrenia have confirmed early speculations that the brain is disordered in schizophrenia. There is also a growing body of evidence suggesting that a disturbance in connectivity between different brain regions, rather than abnormalities within the separate regions themselves, are responsible for the clinical symptoms and cognitive dysfunctions observed in this disorder. Thus an interest in white matter fiber tracts, subserving anatomical connections between distant, as well as proximal, brain regions, is emerging. This interest coincides with the recent advent of diffusion tensor imaging (DTI), which makes it possible to evaluate the organization and coherence of white matter fiber tracts. This is an important advance as conventional MRI techniques are insensitive to fiber tract direction and organization, and have not consistently demonstrated white matter abnormalities. DTI may, therefore, provide important new information about neural circuitry, and it is increasingly being used in neuroimaging studies of psychopathological disorders. Of note, in the past five years 18 DTI studies in schizophrenia have been published, most describing white matter abnormalities. Questions still remain, however, regarding what we are measuring that is abnormal in this disease, and how measures obtained using one method correspond to those obtained using other methods? Below we review the basic principles involved in MR-DTI, followed by a review of the different methods used to evaluate diffusion. Finally, we review MR-DTI findings in schizophrenia.