Iterative deformable finite element model for nonrigid 3D PET/MRI breast image registration

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Andrzej Krol

Second Advisor

James A. Mandel

Third Advisor

Pramod K. Varshney


Iterative, Deformable, Finite element, Nonrigid, PET/MRI, Breast, Image registration

Subject Categories

Biomedical | Electrical and Computer Engineering | Radiology


A new nonrigid 3D medical breast-image registration approach that relies on a finite element method (FEM) and a set of fiducial skin markers (FSMs) placed on the breast surface is presented. This method can be applied for both intra- and intermodal breast image registration. The registration model consists of two steps. In the first step, the locations and displacements of corresponding FSMs observed in both moving and target volumes are determined, and then FEM is used to distribute the FSM displacements linearly over the entire breast volume. The FEM model relies on the analogy between the Cartesian components of the displacement field, and a temperature field in steady state heat transfer (SSHT) in solids. This analogy is valid because the displacement field components in the x, y, and z directions and the temperature field in SSHT can both be modeled using Laplace's equation. The problem can thus be solved via standard heat-conduction FEM software, with arbitrary conductivity of surface elements set much higher than that of volume elements. After determining the displacements at all nodes, the moving breast volume is registered to the target breast volume using an image-warping algorithm. In the second step, to correct for any residual surface misregistration in areas away from FSMs, displacements are estimated for a large number of corresponding surface points on the moving and the target breast images, already aligned in 3D, and our SSHT FEM model and the warping algorithm are applied again.

Resulting registered images have been analyzed using both qualitative and quantitative methods. Three different qualitative similarity estimates named the isoprojected surface similarity (ISS), the normalized polar surface similarity (NPSS), and the z-axis surface similarity (ZSS) were implemented. Convergence and sensitivity analyses were performed via target registration error studies. The performance of our method was also evaluated quantitatively by applying intensity based similarity measures including: the normalized mutual information (NMI), the normalized correlation coefficient (NCC) and the sum of absolute valued differences (SAVD) before and after applications of the method. Our results indicate that the method yields excellent performance with target registration errors comparable with pertinent imaging system spatial resolution.


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