Uniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryOffice of Naval Research / N00014-79-C-042

Model-based reconstruction of accelerated quantitative magnetic resonance imaging (MRI)

Quantitative MRI refers to the determination of quantitative parameters (T1,T2,diffusion, perfusion etc.) in magnetic resonance imaging (MRI). The ’parameter maps’ are estimated from a set of acquired MR images using a parameter model, i.e. a set of mathematical equations that describes the MR images as a function of the parameter(s). A precise and accurate highresolution estimation of the parameters is needed in order to detect small changes and/or to visualize small structures. Particularly in clinical diagnostics, the method provides important information about tissue structures and respective pathologic alterations. Unfortunately, it also requires comparatively long measurement times which preclude widespread practical applications. To overcome such limitations, approaches like Parallel Imaging (PI) and Compressed Sensing (CS) along with the model-based reconstruction concept has been proposed. These methods allow for the estimation of quantitative maps from only a fraction of the usually required data. The present work deals with the model-based reconstruction methods that are applicable for the most widely available Cartesian (rectilinear) acquisition scheme. The initial implementation was based on accelerating the T*2 mapping using Maximum Likelihood estimation and Parallel Imaging (PI). The method was tested on a Multiecho Gradient Echo (MEGE) T*2 mapping experiment in a phantom and a human brain with retrospective undersampling. Since T*2 is very sensitive to phase perturbations as a result of magnetic field inhomogeneity further work was done to address this. The importance of coherent phase information in improving the accuracy of the accelerated T*2 mapping fitting was investigated. Using alternating minimization, the method extends the MLE approach based on complex exponential model fitting which avoids loss of phase information in recovering T*2 relaxation times. The implementation of this method was tested on prospective(real time) undersampling in addition to retrospective. Compared with fully sampled reference scans, the use of phase information reduced the error of the accelerated T*2 maps by up to 20% as compared to baseline magnitude-only method. The total scan time for the four times accelerated 3D T*2 mapping was 7 minutes which is clinically acceptable. The second main part of this thesis focuses on the development of a model-based super-resolution framework for the T2 mapping. 2D multi-echo spin-echo (MESE) acquisitions suffer from low spatial resolution in the slice dimension. To overcome this limitation while keeping acceptable scan times, we combined a classical super-resolution method with an iterative model-based reconstruction to reconstruct T2 maps from highly undersampled MESE data. Based on an optimal protocol determined from simulations, we were able to reconstruct 1mm3 isotropic T2 maps of both phantom and healthy volunteer data. Comparison of T2 values obtained with the proposed method with fully sampled reference MESE results showed good agreement. In summary, this thesis has introduced new approaches to employ signal models in different applications, with the aim of either accelerating an acquisition, or improving the accuracy of an existing method. These approaches may help to take the next step away from qualitative towards a fully quantitative MR imaging modality, facilitating precision medicine and personalized treatment

Fusion of magnetic resonance and ultrasound images for endometriosis detection

Endometriosis is a gynecologic disorder that typically affects women in their reproductive age and is associated with chronic pelvic pain and infertility. In the context of pre-operative diagnosis and guided surgery, endometriosis is a typical example of pathology that requires the use of both magnetic resonance (MR) and ultrasound (US) modalities. These modalities are used side by sidebecause they contain complementary information. However, MRI and US images have different spatial resolutions, fields of view and contrasts and are corrupted by different kinds of noise, which results in important challenges related to their analysis by radiologists. The fusion of MR and US images is a way of facilitating the task of medical experts and improve the pre-operative diagnosis and the surgery mapping. The object of this PhD thesis is to propose a new automatic fusion method for MRI and US images. First, we assume that the MR and US images to be fused are aligned, i.e., there is no geometric distortion between these images. We propose a fusion method for MR and US images, which aims at combining the advantages of each modality, i.e., good contrast and signal to noise ratio for the MR image and good spatial resolution for the US image. The proposed algorithm is based on an inverse problem, performing a super-resolution of the MR image and a denoising of the US image. A polynomial function is introduced to modelthe relationships between the gray levels of the MR and US images. However, the proposed fusion method is very sensitive to registration errors. Thus, in a second step, we introduce a joint fusion and registration method for MR and US images. Registration is a complicated task in practical applications. The proposed MR/US image fusion performs jointly super-resolution of the MR image and despeckling of the US image, and is able to automatically account for registration errors. A polynomial function is used to link ultrasound and MR images in the fusion process while an appropriate similarity measure is introduced to handle the registration problem. The proposed registration is based on a non-rigid transformation containing a local elastic B-spline model and a global affine transformation. The fusion and registration operations are performed alternatively simplifying the underlying optimization problem. The interest of the joint fusion and registration is analyzed using synthetic and experimental phantom images