160 likes | 256 Views
Optimal MR Pulse Sequence Design for Tissue Density and Field Inhomogeneity Estimation. Zhuo Zheng Advanced Optimization Lab, McMaster University Joint work with
E N D
Optimal MR Pulse Sequence Design forTissue Density and Field Inhomogeneity Estimation Zhuo Zheng Advanced Optimization Lab, McMaster University Joint work with Prof. Christopher Anand and Prof. Tamas Terlaky
Motivation • Tissue density: segmentation v.s. estimation. • Field mapping in order to eliminate inhomogeneities. • Optimization applied to medical imaging area (Multidisciplinary in nature). • Scientific evidence for clinical applications.
Tissue Density Estimation Prototype • For a sample voxel: Tissue types Signals
Pulse Sequence (Steady-State Free Precession) • Fast scanning, high resolution and good SNR. • Tissue Properties Design Variables • The dynamic system satisfies: • Therefore:
Model Components • Based on the physical mechanisms, we have:
Imaging • We have • The transformation from tissue densities to measurements:
Objective and Formulation • Unbiased maximum likelihood estimator: • Error given by , white noise • Objective: Choose design variables so that the error in the reconstructed tissue densities is minimized:
SDO Problem • Applying Singular Value Decomposition:
A Clinical Application • Carotid artery tissue densities estimation • We reconstruct the tissue densities based on the optimal solutions obtained by our formulation.
What if field inhomogeneities exist? • Signal measurements become: • Least squares formulation: Numerical results show that it does work !
Numerical Experiment • We discretize the continuous magnetic field to perform our experiment • We simulate the field inhomogeneity for a random pixel
A priori Information • The field inhomogeneity term : smooth and continuous (Maxwell’s Equation). • Tissue density: piece-wise differentiable • The original image would be the one with the least total variation
Conclusions and Future Work • An innovative approach for tissue densities estimation by taking into account many parameters using optimization methods. • An integrated model to estimate both tissue densities and field inhomogeneities. • Many interesting applications of our method, such as brain development studies in infants. • Develop an embedded solver and work with clinical partners.