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Deformable Image Registration / Warping

A - Mid-ventricle contrast-enhanced MRI image of the left ventricle. The hyperenhancement indicates the location of the infarction (arrow in left panel). B - Circumferential stretch distribution for systolic contraction filling. The arrow indicates the infarcted area of the lateral wall does not contract during systole. Mid-ventricle slices of the 3D cine MRI image data used for the systolic function analysis. C - Mid-systolic image (template). D - End-systolic image (target).

Anatomical warping grew primarily out of the pattern recognition field where significant effort has been devoted to the representation of image ensembles. The general approach is to determine the transformation that is necessary to register or align two image datasets by deforming a typical image template into alignment with a target image of interest. The initial applications were to identify corresponding regions between the images. The classic example has been correlation of functional regions in the brain that are well-characterized in term of neuroanatomy with those in a target image that may represent a brain that has pathology in terms of development or disease. The approaches that are used are usually classified as either model-based or pixel-based. Model-based approaches typically require some segmentation of a surface in the 3D image dataset. This surface is then warped into alignment with features in the target image. The pixel-based approaches do not in general require segmentation, but rather deform pixels or some sampling of the pixels. The latter approach is the one utilized in our technique.

In early work, a common approach was to move pixels associated with the template image to new spatial locations to reproduce, in a maximum likelihood sense, target images. The unconstrained registration problem is ill-posed (in the sense that multiple solutions exist) and ad hoc regularization methods are often used to restrict the solution space. In some work this is achieved using analogies to physical materials by treating the original template image as an elastic sheet or a viscous fluid. The latter approach has been extremely successful at 3D registration of complex neuroanatomies via warping. However, the technique as implemented relies on a "mass insertion" term in the momentum equation - this can lead to erroneous estimates of strain and a singular mapping (not one-to-one). Also, the large deformations that occur due to the fluid constitutive assumption can result in large movements of material from one location to another. In general, approaches that rely on defining the template image as a deformable continuum benefit from the fact that the mapping from template to target is guaranteed to be one-to-one on the basis of the fundamentals of deformations as defined in continuum mechanics.

Fiber stretch distribution for the forward (left) and warping (right) analyses. The locations for the sensitivity analysis are shown on the forward model as numbers 1-4. Locations 5-8 are at the same locations as 1-4 but at the mid-ventricle level.

Our approach to Warping is developed around the idea of a deformable template continuum composed of a hyperelastic material (although any other objective material representation may be readily incorporated). A Lagrangian description of the motion is used rather than the Eulerian description used in previous work. The current approach is implemented in a general-purpose nonlinear finite element program, and thus is ideal for nearly any type of solid material model, while including some or all boundary conditions if known. Further, the method automatically computes the stress tensor as part of the equilibrium search and thus stresses are available at all points in the deformed template domain after registration. The stresses are of interest when using the technique to regularize ill-posed problems in mechanics or when the constitutive behavior is well-defined; for strain measurement applications the stresses and constitutive model serve to regularize the problem.

3D Registration of Mouse Brain MRI

• Publications -- Deformable Image Registration
• Image Gallery -- Deformable Image Registration

Principal Researchers:

• Dr. Jeff Weiss