James A. Mandel

MRI/PET nonrigid breast-image registration using skin fiducial markers.

We propose a finite-element method (FEM) deformable breast model that does not require elastic breast data for nonrigid PET/MRI breast image registration. The model is applicable only if the stress conditions in the imaged breast are virtually the same in PET and MRI. Under these conditions, the observed intermodality displacements are solely due the imaging/reconstruction process. Similar stress conditions are assured by use of an MRI breast-antenna replica for breast support during PET, and use of the same positioning. The tetrahedral volume and triangular surface elements are used to construct the FEM mesh from the MRI image. Our model requires a number of fiducial skin markers (FSM) visible in PET and MRI. The displacement vectors of FSMs are measured followed by the dense displacement field estimation by first distributing the displacement, vectors linearly over the breast surface and then distributing them throughout the volume. Finally, the floating MRI image is warped to a fixed PET image, by using an appropriate shape function in the interpolation from mesh nodes to voxels. We tested our model on an elastic breast phantom with simulated internal lesions and on a small number of patients imaged, with FMS using PET and MRI. Using simulated lesions (in phantom) and real lesions (in patients) visible in both PET and MRI, we established that the target registration error (TRE) is below two pet voxels.

Computerized method for nonrigid MR-to-PET breast-image registration.

We have developed and tested a new simple computerized finite element method (FEM) approach to MR-to-PET nonrigid breast-image registration. The method requires five-nine fiducial skin markers (FSMs) visible in MRI and PET that need to be located in the same spots on the breast and two on the flanks during both scans. Patients need to be similarly positioned prone during MRI and PET scans. This is accomplished by means of a low gamma-ray attenuation breast coil replica used as the breast support during the PET scan. We demonstrate that, under such conditions, the observed FSM displacement vectors between MR and PET images, distributed piecewise linearly over the breast volume, produce a deformed FEM mesh that reasonably approximates nonrigid deformation of the breast tissue between the MRI and PET scans. This method, which does not require a biomechanical breast tissue model, is robust and fast. Contrary to other approaches utilizing voxel intensity-based similarity measures or surface matching, our method works for matching MR with pure molecular images (i.e. PET or SPECT only). Our method does not require a good initialization and would not be trapped by local minima during registration process. All processing including FSMs detection and matching, and mesh generation can be fully automated. We tested our method on MR and PET breast images acquired for 15 subjects. The procedure yielded good quality images with an average target registration error below 4mm (i.e. well below PET spatial resolution of 6-7 mm). Based on the results obtained for 15 subjects studied to date, we conclude that this is a very fast and a well-performing method for MR-to-PET breast-image nonrigid registration. Therefore, it is a promising approach in clinical practice. This method can be easily applied to nonrigid registration of MRI or CT of any type of soft-tissue images to their molecular counterparts such as obtained using PET and SPECT.

Iterative finite element deformable model for nonrigid coregistration of multimodal breast images

We have developed a nonrigid registration technique applicable to breast tissue imaging. It relies on a finite element method (FEM) model and a set of fiducial skin markers (FSMs) placed on the breast surface. It can be applied for both intra- and intermodal breast image registration. The registration consists of two steps. First, location and displacements of corresponding FSM 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. After determining the displacements at all the mesh 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 misregistration, 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 FEM model and the warping algorithm are applied again. Our non-rigid multimodality and intramodality breast image registration method yielded good quality images with target registration error comparable with pertinent imaging system spatial resolution

Micromechanical studies of crack growth in fiber reinforced materials

Abstract A two dimensional, parametric, micromechanical finite element study of the stress conditions near a crack tip in a fiber reinforced isotropic material was performed. The variables considered include the mechanical properties of the isotropic matrix material, fibers, and interface between the fibers and matrix material and the geometry of the composite. Experimental studies, using methyl methacrylate matrix material reinforced with carefully placed steel fibers were conducted. The close agreement between finite element and experimental values for the loading required for both the initiation of crack growth in the matrix material and crack arrest by the fibers show that micromechanical finite element studies are applicable for the development of engineering models for the fracture toughness of fiber reinforced material. From the parametric finite element studies it was concluded that: 1. (1) A small percentage by volume of higher modulus fibers can result in a significant reduction in opening mode stresses in the matrix material near a crack tip. Thus the presence of the fibers can result in crack arrest and an increase in the effective fracture toughness. 2. (2) In general, shear stresses in the matrix material adjacent to the fiber and bond stresses between the fibers and matrix material are larger for a shear mode loading than for an opening mode loading. Although these stresses may not directly result in crack growth, they may cause fiber delamination which in turn may result in unstable crack growth. Thus for studies of effective fracture toughness, mixed mode loadings must be considered.

Micromechanical multiplane finite element modeling of crack growth in fiber reinforced materials

Abstract The purpose of this study was to devise and verify a scheme of analysis which can be used to investigate the micromechanical failure mechanisms and determine an effective fracture toughness for a class of fiber reinforced materials. The material of primary interest in this study consists of a linearly elastic matrix material reinforced with rows of parallel, linearly elastic and straight fibers. Micromechanical multiplane finite element and experimental studies of the stress conditions near a crack front in a side cracked fiber reinforced epoxy tensile specimen were conducted. The 2-D multiplane method of analysis, recently developed at Syracuse University for approximate analysis of a class of 3-D problems, was the basis of the micromechanical finite element analytical technique developed in this study. Since failure of a member fabricated from a fiber reinforced material is generally proceeded by local failures, sequential finite element analyses were performed to model the progressive failure mechanism. Local failure modes considered in the analysis are yield in either the matrix material or fibers, crack extension in the matrix material, and failure of the matrix to fiber bond. The agreement between the multiplane analytical and laboratory test results show that the multiplane method provides a useful tool for micromechanical study of fiber reinforced composite materials.

Deformable model for 3D intramodal nonrigid breast image registration with fiducial skin markers

We implemented a new approach to intramodal non-rigid 3D breast image registration. Our method uses fiducial skin markers (FSM) placed on the breast surface. After determining the displacements of FSM, finite element method (FEM) is used to distribute the markers’ displacements linearly over the entire breast volume using the analogy between the orthogonal components of the displacement field and a steady state heat transfer (SSHT). It is valid because the displacement field in x, y and z direction and a SSHT problem can both be modeled using LaPlace’s equation and the displacements are analogous to temperature differences in SSHT. It can be solved via standard heat conduction FEM software with arbitrary conductivity of surface elements significantly higher than that of volume elements. After determining the displacements of the mesh nodes over the entire breast volume, moving breast volume is registered to target breast volume using an image warping algorithm. Very good quality of the registration was obtained. Following similarity measurements were estimated: Normalized Mutual Information (NMI), Normalized Correlation Coefficient (NCC) and Sum of Absolute Valued Differences (SAVD). We also compared our method with rigid registration technique.

Gold cylinder fiber biosensor

We have fabricated and tested Gold Cylinder Fiber (GCF) bio sensors. The sensor fiber has a thin, approximately 3 nm to 5 nm thick, Gold alloy film layer at the glass core glass cladding boundary. One end of the fiber is etched to let the gold alloy cylinder protrude about 10 m. A Single Mode Fiber (SMF) is connected to the other end of the GCF. Light propagates through the SMF to a short section of GCF. The etched end of the GCF is dipped into the fluid to be analyzed. The reflected light from the sample returns back through the SMF to a spectrum analyzer.

Registration of parametric dynamic F-18-FDG PET/CT breast images with parametric dynamic Gd-DTPA breast images

This study was undertaken to register 3D parametric breast images derived from Gd-DTPA MR and F-18-FDG PET/CT dynamic image series. Nonlinear curve fitting (Levenburg-Marquardt algorithm) based on realistic two-compartment models was performed voxel-by-voxel separately for MR (Brix) and PET (Patlak). PET dynamic series consists of 50 frames of 1-minute duration. Each consecutive PET image was nonrigidly registered to the first frame using a finite element method and fiducial skin markers. The 12 post-contrast MR images were nonrigidly registered to the precontrast frame using a free-form deformation (FFD) method. Parametric MR images were registered to parametric PET images via CT using FFD because the first PET time frame was acquired immediately after the CT image on a PET/CT scanner and is considered registered to the CT image. We conclude that nonrigid registration of PET and MR parametric images using CT data acquired during PET/CT scan and the FFD method resulted in their improved spatial coregistration. The success of this procedure was limited due to relatively large target registration error, TRE = 15.1±7.7 mm, as compared to spatial resolution of PET (6-7 mm), and swirling image artifacts created in MR parametric images by the FFD. Further refinement of nonrigid registration of PET and MR parametric images is necessary to enhance visualization and integration of complex diagnostic information provided by both modalities that will lead to improved diagnostic performance.

Iterative deformable FEM model for nonrigid PET/MRI breast image coregistration

We implemented an iterative nonrigid registration algorithm to accurately combine functional (PET) and anatomical (MRI) images in 3D. Our method relies on a Finite Element Method (FEM) and a set of fiducial skin markers (FSM) placed on breast surface. The method is applicable if the stress conditions in the imaged breast are virtually the same in PET and MRI. In the first phase, the displacement vectors of the corresponding FSM observed in MRI and PET are determined, then FEM is used to distribute FSM displacements linearly over the entire breast volume. Our FEM model relies on the analogy between each of the orthogonal components of displacement field, and the temperature distribution field in a steady state heat transfer (SSHT) in solids. 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 mesh nodes, moving (MRI) breast volume is registered to target (PET) breast volume using an image-warping algorithm. In the second iteration, to correct for any residual surface and volume misregistration, a refinement process is applied to the moving image, which was already grossly aligned with the target image in 3D using FSM. To perform this process we determine a number of corresponding points on each moving and target image surfaces using a nearest-point approach. Then, after estimating the displacement vectors between the corresponding points on the surfaces we apply our SSHT model again. We tested our model on twelve patients with suspicious breast lesions. By using lesions visible in both PET and MRI, we established that the target registration error is below two PET voxels. The surface registration error is comparable to the spatial resolution of PET.

Zero thickness quarter point crack tip finite element for modeling an interface between two materials

Abstract A zero thickness quarter point crack tip element for modeling the interface crack between two materials is presented. The stiffness matrix of the element is derived. The element is shown to have the theoretical 1/√ r singularity in the stress field at the crack tip and is compatible with other singular quadratic quarter point elements. Numerical results are in close agreement under biaxial tension, K I is insensitive and K II is sensitive to the changes in the shear stiffness of the interface bond.